Junior high school mathematics training equation

1. Fill in the blanks: (2 '× 1 1 = 22')

1, the root of the equation x2 = is.

2. The general form of the equation (x+1) 2-2 (x-1) 2 = 6x-5 is.

3. One root of the quadratic equation x2+mx+3=0 about x is 1, so the value of m is.

4. Given that the quadratic trinomial x2+2mx+4-m2 is completely flat, then m=.

5. It is known that +(b- 1) 2 = 0. When k is, the equation kx2+ax+b=0 has two unequal real roots.

6. The equation mx2-2x+ 1 = 0 about x has only one real root, then m=.

7. Please write that one root is 1 and the other root satisfies-1

8. Equation X X2-(2m2+m-6) X-m= 0 If two mutually opposite numbers, then m=.

9. It is known that the two roots of the unary quadratic equation (A- 1) x2+x+A2- 1 = 0 are x 1, x2, x 1+x2=, then x 1, x2=.

10 The original timber stock of a timber yard is one cubic meter, and it is known that the timber grows at a rate of 20% every year. When the amount of timber felled in winter is X cubic meters each year, the stock of timber is cubic meters after one year and B cubic meters after two years. Try to write the relationship between a, b and m:

Second, multiple-choice questions: (3 '× 8 = 24')

1 1, the equation about x (m+ 1) x2+2mx-3 = 0 is a quadratic equation, so the value of m is ().

A, any real number b, m≠ 1 C, m ≠- 1 d, m>- 1

12. The following is a fill-in-the-blank question that a classmate answered in a math exam. The correct answer is ().

A, if x2=4, then x=2 B, if 3x2=bx, then x=2.

A root of c, x2+x-k=0 is 1, then k=2.

If the value of the fraction is zero, then x=2.

13, the root of equation (x+3) (x-3) = 4 is ().

A, there is no real number root b, there are two unequal real number roots c, two are reciprocal d, and two are opposites.

The sum of all real roots of 14, unary quadratic equation x2-3x- 1 = 0, x2+4x+3=0 is equal to ().

a 、- 1 B 、-4 C、4 D、3

15, known equation () 2-5 ()+6 = 0, let =y become ().

a、y2+5y+6=0 B、y2-5y+6=0 C、y2+5y-6=0 D、y2-5y-6=0

16. The turnover of a supermarket in January was 1 10,000 yuan, and the turnover in the first quarter was * * * 8 million yuan. If the average monthly growth rate is x, the listed equation should be ().

a、 100( 1+x)2=800 B、 100+ 100×2x=800 C、 100+ 100×3x=800 D、 100[ 1+( 1+x)+( 1+x)2]

17, given that quadratic equation 2x2-3x+3=0, then ()

A, the sum of two roots is-1.5b, the difference between two roots is-1.5c, the product of two roots is-1.5d, and there is no real root.

18, A2+A2- 1 = 0, B2+B2- 1 = 0 and a≠b, then ab+a+b= ().

a、2 B、-2 C、- 1 D、0

3. Solve the following equation: (5 '× 5 = 25')

19, (x-2) 2-3 = 0 20, 2x2-5x+ 1 = 0 (matching method)

2 1、x(8+x)= 16 22、

23 、( 2x-3)2-2(2x-3)-3=0

Fourth, answer questions.

24. It is known that the two sides of a triangle are 3 and 8 respectively, and the value of the third side is the root of the unary quadratic equation X2- 17x+66 = 0. Find the perimeter of this triangle. (6')

25. A lighting store purchased a batch of energy-saving lamps of a certain model and used them in 400 yuan. During the handling, five lamps were accidentally broken. The store sold all the remaining lamps at high prices in 4 yuan, and then used the proceeds to buy a batch of such energy-saving lamps at the same price as last time, but the number of lamps purchased was 9 more than last time. Ask about the purchase price of each lamp. (6')

26. In RT △ABC, ∠ c = 90, hypotenuse c = 5°, and the lengths of two right angles A and B are two quadratic equations about x x2-MX+2m-2 = 0 .( 1) Find the value of m (2) Find the area of △ ABC (3) Find the smaller acute angle. (8')

The name of 1, the training problem of one-dimensional quadratic equation in grade three.

1. Fill in the blank: (3 points for 3, 4 and 5, 2 points for the rest, ***39 points)

This equation is converted into the general formula:

2. In the equation about, the quadratic term is; The constant term is;

The main terms are:

3. The root of the equation is: the root of the equation is:

The root of the ⒌ equation is:

⒍ ⒎

⒏ ⒐

Second, multiple-choice questions (6 points× 3 =18 points)

1. When selecting equations, the number of quadratic equations in one variable should be-().

A 3 B 4 C 5 D 6