3x^2-4x-4=0.

(2y+ 1)^2+3(2y+ 1)+2=0.

(x-2)^2-3=0

2x^2-5x+ 1=0

x(8+x)= 16

(2x-3)^2-2(2x-3)-3=0

x^2- 17x+66=0

(x+ 1)^2-2(x- 1)^2=6x-5

4(x+2)^2=9(2x- 1)^2

It is known that x square +X+ 1=0, then x square+1/X square (that is, one third of x square) =?

1. If there is a point C on the line segment AB, the length is 10 (radical number 5+ 1)cm, and AC 2 = AB * BC, then AC is long?

2. A hotel has 65,438+040 rooms. Every room is full every day when we rent 60 yuan. If the daily rent of a room increases by 5 yuan, the number of rooms will decrease by five. When the daily rent of each room is RMB, the total daily rent will be as high as RMB 654.38+0 million? .

3. In the isosceles triangle ABC, the length of. BC=6。 AB.AC are two integer roots of the equation x 2- 10x+m = 0, so find m.

4. Can a 22㎝ long wire be folded into a rectangle of 32 square centimeters? Give reasons

5. If A is a rational number, try to find out whether the root of the unary quadratic equation X 2+3 (A- 1) X+(2A 2+A+B) = 0 is a rational number when b is a value.

6. Let the unary quadratic equation 3 (m-2) y 2-2 (m+1) y-m = 0 have positive integer roots, and find the integer m satisfying the conditions.

First, multiple-choice questions:

1, the following equation (1)-x2+2 = 0 (2) 2x2-3x = 0 (3)-3x2 = 0 (4) x2+= 0 (5) = 5x (6) 2x2-3 =

A, two B's, three C's, four D's and five.

2, the following formula is correct ()

x2+3x =(x+)2-(2)x2+2x+5 =(x+ 1)2+4

(3)x2-x+=(x-)2+(4)3 x2+6x+ 1 = 3(x+ 1)2-2

a，( 1)(3) B，(2)(4) C，( 1)(4) D，(2)(3)

3. Equation (x- 1)2+(2x+ 1)2=9x The coefficient of the first term is ().

a，2 B，5 C，-7 D，7

4. The equation x2-3x+2-m=0 has a real root, so the range of m is ().

a，m & gt- B，m≥ C，m≥- D，m & gt

5. Equation (m+1) x2-(2m+2) x+3m-1= 0 has a root of 0, so the value of m is ().

a，B，C，- D，-

6. The difference between the big root and the small root of the equation x2-mx+=0 is ().

a，0 B， 1 C，m D，m+ 1

7. If the equation 3ax2-2(a- 1)x+a=0 about x has a real root, then the range of a is ().

A, a< and a≠0 B, a≥ C, a≤ and a≠0 D, a≤

8. If the equation 2x(kx-4)-x2+6=0 has no real root, then the minimum integer value of k is ().

a， 1 B，2 C，3 D，4

9. One of the unary quadratic equations is 8 larger than the other, and the sum of the two is 6, then this equation is ().

a、x2-6x-7=0 B、x2-6x+7=0 C、x2+6x-7=0 D、x2+6x+7=0

10, equation 3=2x-6 is to be converted into rational equation ().

a，4x2-33x+54=0 B，4x2-27x+42=0 C，4x2+2 1x+42=0 D，4x2-33x+38=0

1 1, and the equation 3x2+ 15x+2=2 is transformed into an integral equation by substitution. Among the following substitutions, the correct one is ().

a，=y B，3x2+ 15x=y C，=y D，x2+5x+ 1=y

12, remove the denominator to solve the equation about x, and add the root, then the value of m is ().

A, 2 B, 1 C,-1 D, none of the above answers are correct.

13. Among the following four groups of numbers, the group that is the solution of the system of equations is ().

A, ① and ④ B, ② and ④ C, ① and ② D, ③ and ④.

14, the equations are known, and there are two equal real number solutions, then the value of m is ().

a， 1 B，- 1 C， 1D

Second, fill in the blanks:

Transforming the equation x2+=x+x into a general form is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

Decomposition factor in real number range: 2x2-4x-3 = _ _ _ _ _ _ _.

If one root of equation 8x2-(k- 1)x+k-7 =0, then k = _ _ _ _ _ _ _

A quadratic equation with the root of _ _ _ _ _ _ _.

If the cost of producing a drug is planned to be reduced to 8 1% within two years, the average annual reduction percentage is _ _ _ _ _.

If X 1 and X2 are two of the equations 2x2-7x+4=0, then the values of x 1 and x2+X22 are _ _ _ _ _ _ _.

It is known that the sum of two equations about X x2+ax+ 1-a2=0 is equal to 3a-8, so the product of them is equal to _ _ _ _ _ _ _.

Third, solve the equation. 6(x2+)+5(x+)-38=0

Four, the two prime numbers P and Q are the values of the two roots of the equation x2-99x+m=0.

One-dimensional quadratic equation test questions

1. Fill in the blanks: (3 points for each question, ***30 points)

1, equation (x- 1)(2x+ 1)=2, and its quadratic coefficient is.

2. The equation about X is (m2-1) x2+(m-1) x-2 = 0, so when m, the equation is a quadratic equation;

When m, the equation is a linear equation.

3. If the equation has an increasing root, then the increasing root X = _ _ _ _ _ _, and m=.

4. (Guiyang, 2003) It is known that the equation has two equal real roots, so the acute angle = _ _ _ _ _ _.

5. If the equation kx2-6x+ 1=0 has two real roots, the range of k is.

6. Let x 1 and x2 be the two roots of equation 3x2+4x-5=0, then x 12+x22 =.

7. Equation 2x2+(m2-9)x+m+ 1=0 About x, when m=, the two roots are reciprocal;

When m=, the two roots are opposite to each other.

8. If x 1 = is the root of quadratic equation x2+ax+ 1=0, then a=,

The other root of the equation x2 =.

9. The equation x2+2x+a- 1=0 has two negative roots, so the range of a is.

10, if p2-3p-5=0, Q2-3q-5 = 0, p≠q, then.

Second, multiple-choice questions: (3 points for each small question, *** 15 points)

1, and the root of the equation is ()

(a) The equation has two unequal real roots; (b) This equation has two equal real roots.

(c) The equation has no real root. (d) The root of the equation is related to the value of.

2, known equation, the following statement, the correct is ().

(a) The sum of the two equations is 1 (B) The product of the two equations is 2.

(c) The sum of the two equations is-1 (d) The product of the two equations is twice the sum of the two equations.

3. Assuming that both roots of the equation are integers, the value of can be ().

(A)- 1 (B) 1 (C)5 (D) Any of the above three.

4. If the roots of the quadratic equation x2+px+q=0 about x are X 1 = 3 and X2 = 1 respectively, then this quadratic equation is ().

A.x2+3x+4 = 0 b . x2-4x+3 = 0 c . x2+4x-3 = 0d . x2+3x-4 = 0

5. When using the matching method to solve the following equations, the wrong formula is ().

A.x2-2x-99=0 to (x-1) 2 =100b.x2+8x+9 = 0 to (x+4)2=25.

C.2t2-7t-4=0 to D.3y2-4y-2=0 to 0.

Third, solve the following equation: (5 points for each small question, ***30 points)

( 1) (2)

(3) (4)4x2-8x+ 1=0 (matching method)

(5) 3x2+5(2x+ 1)=0 (according to the formula) (6)

Four, (this question 6 points)

A chemical fertilizer plant in Ningxia (2003) produced 500 tons of chemical fertilizer in April last year. Due to poor management, the output decreased 10% in May. Since June, the output has increased month by month, reaching 648 tons in July. So, what is the average growth rate of output in June and July?

V. (6 points for this question)

There is a conference room, 20 meters long and 0/5 meters wide, with a carpet in the middle. The area of the carpet is half that of the conference room, and the width of the blank space around the carpet is the same. What is the width of the blank?

Six, (this question 6 points)

(Nanjing, 2003) A lighting store purchased a batch of energy-saving lamps of a certain model and used them in 400 yuan. In the process of handling, five lights were accidentally broken. The store sold all the remaining 4 yuan lamps at a high price, and then used the money to buy a batch of such energy-saving lamps. The purchase price was the same as last time, but the number of purchases was 9 more than last time. Ask about the purchase price of each lamp.

Vii. (This title is 12, in which the first title (1) is 7, and the second title is additional title (5))

(Weifang, 2003) As shown in the figure, in △ABC, AB=6 cm, BC=8 cm, ∠ B = 90, point P starts from point A and moves along the AB side to point B at a speed of 1 cm/s, and point Q starts from point B and moves along the BC side to point C at a speed of 2 cm/s.

(1) If P and Q start from A and B at the same time, how many seconds does it take to make the area of △PBQ equal to 8 square centimeters?

(2) (Additional Question) If P and Q start from A and B respectively, P will move on the side of BC after arriving at B. After a few seconds, is the area of △PCQ equal to 12.6 cm2?

1. Fill in the blanks: (3 points for each question, ***30 points)

1, the equation (x–1) (2x+1) = 2 is in general form, and its quadratic coefficient is.

2. The equation about X is (m2–1) x2+(m–1) x–2 = 0, so when m, the equation is a quadratic equation;

When m, the equation is a linear equation.

3. If the equation has an increasing root, then the increasing root X = _ _ _ _ _ _, and m=.

4. (Guiyang, 2003) It is known that the equation has two equal real roots, so the acute angle = _ _ _ _ _ _.

5. If the equation kx2–6x+1= 0 has two real roots, then the range of k is.

6. Let x 1 and x2 be the two roots of the equation 3x2+4x–5 = 0, then x 12+x22 =.

7. Equation 2x2+(m2–9) x+m+1= 0, when m=, the two roots are reciprocal;

When m=, the two roots are opposite to each other.

8. If x 1 = is the root of quadratic equation x2+ax+ 1=0, then a=,

The other root of the equation x2 =.

9. If the equation x2+2x+a–1= 0 has two negative roots, then the range of a is.

10, if p2–3p–5 = 0, Q2–3q–5 = 0, p≠q, then.

Second, multiple-choice questions: (3 points for each small question, *** 15 points)

1, and the root of the equation is ()

(a) The equation has two unequal real roots; (b) This equation has two equal real roots.

(c) The equation has no real root. (d) The root of the equation is related to the value of.

2, known equation, the following statement, the correct is ().

(a) The sum of the two equations is 1 (B) The product of the two equations is 2.

(c) The sum of the two equations is-1 (d) The product of the two equations is twice the sum of the two equations.

3. Assuming that both roots of the equation are integers, the value of can be ().

(a)-1(b)1(c) 5 (d) Any of the above three.

4. If the roots of the quadratic equation x2+px+q=0 about x are X 1 = 3 and X2 = 1 respectively, then this quadratic equation is ().

A.x2+3x+4 = 0 b . x2-4x+3 = 0 c . x2+4x-3 = 0d . x2+3x-4 = 0

5. When using the matching method to solve the following equations, the wrong formula is ().

A.x2-2x-99=0 to (x-1) 2 =100b.x2+8x+9 = 0 to (x+4)2=25.

C.2t2-7t-4=0 to D.3y2-4y-2=0 to 0.

Third, solve the following equation: (5 points for each small question, ***30 points)

( 1) (2)

(3) (4) 4x2–8x+1= 0 (by matching method)

(5) 3x2+5(2x+ 1)=0 (according to the formula) (6)

Four, (this question 6 points)

A chemical fertilizer plant in Ningxia (2003) produced 500 tons of chemical fertilizer in April last year. Due to poor management, the output decreased 10% in May. Since June, the output has increased month by month, reaching 648 tons in July. So, what is the average growth rate of output in June and July?

V. (6 points for this question)

There is a conference room, 20 meters long and 0/5 meters wide, with a carpet in the middle. The area of the carpet is half that of the conference room, and the width of the blank space around the carpet is the same. What is the width of the blank?

Six, (this question 6 points)

(Nanjing, 2003) A lighting store purchased a batch of energy-saving lamps of a certain model and used them in 400 yuan. In the process of handling, five lights were accidentally broken. The store sold all the remaining 4 yuan lamps at a high price, and then used the money to buy a batch of such energy-saving lamps. The purchase price was the same as last time, but the number of purchases was 9 more than last time. Ask about the purchase price of each lamp.

Vii. (This title is 12, in which the first title (1) is 7, and the second title is additional title (5))

(Weifang, 2003) As shown in the figure, in △ABC, AB=6 cm, BC=8 cm, ∠ B = 90, point P starts from point A and moves along the AB side to point B at a speed of 1 cm/s, and point Q starts from point B and moves along the BC side to point C at a speed of 2 cm/s.

(1) if p and q start from a and b at the same time, how many seconds does it take to make the area of △PBQ equal to 8 square centimeters?

(2) (Additional Question) If P and Q start from A and B respectively, P will move on the side of BC after arriving at B. After a few seconds, is the area of △PCQ equal to 12.6 cm2?