1, it is known that the equation x2-6x+q=0 can be expressed as (x-p)2=7, then x2-6x+q=2 can be expressed as follows: () a, (x-p)2=5 B, (x-p)2=9C, (x-p+).
2. It is known that m is a root of the equation x2-x- 1=0, then the value of the algebraic expression m2-m is equal to ().
a 、- 1 B、0 C、 1 D、2
3. If α and β are two real roots of the equation x2+2x-2005=0, the value of α2+3α+β is ().
A, 2005b, 203c, 205d, 40 10
4. The equation kx2+3x- 1=0 about x has real roots, so the range of k is ().
A, k≤-9999 B, k≥- and k≠0C, k≥- D, k >；; -and k≠0 4444
5. If the two roots of the quadratic equation of x are x 1= 1 and x2=2, then this equation is ().
a、x2+3x-2=0 B、x2-3x+2=0 C、x2-2x+3=0 D、x2+3x+2=0
6. It is known that the equation x2(-2k- 1)x+k2=0 about x has two unequal real roots, so the maximum integer value of k is ().
a 、-2 B 、- 1 C、0 D、 1
At the end of 2004, the green area of a city was 300 hectares. After two years of greening, the green area has increased year by year, reaching 363 hectares by the end of 2006. Let the average annual growth rate of green area be x, and the equation listed in the question is correct ().
a、300( 1+x)=363 B、300( 1+x)2=363
c、300( 1+2x)=363 D、363( 1-x)2=300
8. Two students, A and B, solved the quadratic equation of one variable respectively. Because A misread the coefficient of the first term, two of the equations are -3 and 5, while B misread the constant term, and two are 2+6 and 2-6, so the original equation is ().
a、x2+4x- 15=0 B、x2-4x+ 15=0 C、x2+4x+ 15=0 D、x2-4x- 15=0
9. If the equation x2+mx+ 1=0 and the equation x2-x-m=0 have the same real root, then the value of m is ().
a、2 B、0 C、- 1 D、 1 4
y2？ 5y？ 6=0, then the length of the third side is () 10, and it is known that the lengths of both sides of right triangle X and Y satisfy |x2-4|+
A, 22 or b, 5 or 22 C, or 22 D, 22 or.
Fill in the blanks (3 points for each small question, 30 points for * * *)
1 1. If one root of equation 2x2-3x+c=0 is 1, the other root is.
12, the solution of the unary quadratic equation x2-3x-2=0 is
13, if (2a+2b+1) (2a+2b-1) = 63, then the value of a+b is
In 14 and isosceles △ABC, BC=8, and the lengths of AB and AC are two of the equations x2- 10x+m=0 about X, then the value of m is.
15, the per capita GDP of a city in 2005 is about 1.2 times that of 2003. If the annual per capita GDP growth rate of the city remains unchanged, then the growth rate is.
16. Scientific research shows that when the ratio of the length to the height of a person's lower limbs is 0.6 18, it looks the most beautiful. Adult female height 153cm, lower limb length 92cm. The best height of the high heels worn by this lady is about cm. (accurate to 0. 1cm).
17. The diameter of a well is 2m. Straight into the bottom of the well with bamboo poles, 0.5m higher than the wellhead. If the bamboo pole tends to go deep into the well,
If the wellhead and bamboo pole are just flush with the wellhead, the well depth is m and the bamboo pole length is m.
18, the circumference of a right triangle is 2+
Because.
19. If the equation 3x2-ax+a-3=0 has only one positive root, then a2? 8a？ The value of 16 is.
20. Given that the two roots of the equation x2+3x+ 1=0 are α and β, then 6, and the median line on the hypotenuse is 1, then the value of the area+of this right triangle is.
Iii. Answering questions (***60 points)
2 1, solve the equation (3 points for each small question, *** 12 points)
( 1)(x-5)2 = 16(2)x2-4x+ 1 = 0(3)x3-2 x2-3x = 0(4)x2+5x+3 = 0
22.(8 points) It is known that x 1 and x2 are two real roots of equation x2+(2a- 1)x+a2=0, and (x1+2) (x2+2) =1.
23.(8 points) Equation X2-2 is known about X (m+ 1) X+M2 = 0.
What is the value of (1) equation? Choose a suitable integer for m, so there are two equations.
Unequal real roots, find these two roots.
24.(8 points) It is known that the quadratic equation x2-4x+k=0 has two unequal real roots.
(1) Find the value range of k 2. If k is the largest integer satisfying the condition and quadratic equation x2-4x+k=0.
Same root as x2+mx- 1=0. Find the value of m at this time.
25.(8 points) It is known that A, B and C are opposite sides of ∠A, ∠B and ∠C in △ABC, and the equation (c-b)x2+2(b-a)x+(a-b)=0 about X has two equal real roots. Just try it.
26.(8 points) An engineering team contracted a demolition project during the renovation of shanty towns in our city. It was originally planned to demolish 1250m2 every day. Due to insufficient preparation, the amount of demolition on the first day was reduced by 20%. From the second day, the construction team accelerated the demolition, and on the third day, 1440m2 was demolished.
Q: (1) The daily demolition area of the construction team on the second and third days is the same as that of the previous day. Find this percentage.
27. (points) A fruit wholesale mall sells a high-grade fruit. If the profit per kilogram is 10 yuan, it can sell 500 kilograms every day.
According to market research, if the price per kilogram increases by 1 yuan, the daily sales will be reduced by 20 kilograms.
(1) At present, if shopping malls want to make a profit of 6,000 yuan per day, and at the same time let customers get benefits, how much will the price per kilogram increase?
Yuan? If shopping malls are purely from an economic point of view, how much will the price increase per kilogram of this fruit maximize the profit of shopping malls?
7. The purchase price of a commodity is each piece in 40 yuan, if the selling price is each piece in 50 yuan.
265,438+00 pieces. If the price exceeds that of 50 yuan, but not 80 yuan, the price of each commodity will increase by 65,438+00 yuan, and 65,438+0 pieces will be sold less every month; The price is higher than that of 80 yuan. If the price rises again, for every price increase of 1 yuan, three pieces will be sold less every month. Suppose the price of this commodity is X yuan.
(1), the profit of each commodity is RMB. More than 50 yuan, not 80 yuan, will be sold every month. If it exceeds 80 yuan, it will be sold every month. Fill in the blanks with the formula of X. )
(2) At what price can the profit reach 7200 yuan if it exceeds 50 yuan but not 80 yuan?
(3) If it surpasses 80 yuan, what is the selling price and the profit is 7,500 yuan?
8. When a shopping mall sells a batch of shirts, it can sell an average of 30 shirts a day, and each one earns 50 yuan. In order to expand sales, increase profits and reduce inventory, the shopping center decided to reduce prices. If each piece is reduced by 1 yuan, the mall can sell two more pieces a day on average. If the average daily income of the mall is 2 100, how much is the shirt reduced?
1 1. One-dimensional quadratic equation solving application problem When the goods with unit price of 40 yuan are sold in 50 yuan, 500 units can be sold. If the commodity price increases by 1 yuan, its sales volume will decrease by 10 units. In order to get a profit of 8000 yuan, what price should the store set for this commodity? How much should I buy?
12. With the continuous improvement of people's living standards, the number of family cars in our city has increased year by year. According to statistics, there were 64 family cars in a residential area in 2006, and the number of family cars reached 100 by the end of 2008. (1) If the average annual growth rate of family cars in this community is the same from the end of 2006 to the end of 2009, ask this community.
(2) In order to alleviate the parking contradiction, the community decided to invest 6.5438+0.5 million yuan to build a number of parking spaces. According to estimates, the construction cost of indoor parking spaces is 5000 yuan, and the construction cost of outdoor parking spaces is 654.38+0.000 yuan. Considering practical factors, the number of outdoor parking spaces is not less than 2 times of indoor parking spaces, but not more than 2.5 times of indoor parking spaces, so the community can build up to two kinds of parking spaces. Try to write out all possible schemes.