1. If the equation mx2+2x+ 1=0 about x has two real roots, find the range of m. 。

2. If the two real roots of equation (A2- 1) x2+(A-5) x+3 = 0 are reciprocal, find the value of a. 。

3. If the two real roots of the equation x2+(m2-9) x+m- 1 = 0 are in opposite directions, find the value of m and the root of the equation.

4. It is known that m and n are two real roots of the equation x2-4x+ 1 = 0. How about finding the algebraic expression 2m2+4N2-8n+ 1? Value.

5. It is known that in ABC, the opposite sides of ∠A, ∠B and ∠C are A, B and C respectively, which are related to the quadratic equation of X..

(a+c)x2+bx+ =0 has two equal real roots. It is proved that ABC is RTδ with hypotenuse.

6. When k is taken, does the fractional equation about x have an increasing root?

7. It is known that A, B and C are three sides of ABC, and c=5. The equation (b+c)x2+2ax+(c-b)=0 about X has two equal real roots, and the length of both sides of A and B is the equation x2+(2m- 1) x+m2+3 = 0 about X.

8. There is a rectangular open space on campus, the sum of length and width is one meter, and the length of a diagonal line is b meters. A and B satisfy the equation:

In order to green the campus, we should plant grass in the rectangular open space. Try to calculate the area of rectangular open space.

9. Workers in Group A and Group B finish a certain job together. After 10, because group A has other tasks, group B has to do it alone for another two days to complete the task. What if it's done by one person? Group A can finish the work four days faster than Group B. How many days does it take each of them to finish it alone?

10. If a store buys a batch of goods from a manufacturer at a unit price of 2 1 yuan, the store can set its own price. If the price of a commodity is one yuan, you can sell (350- 10a) pieces, but does the price bureau limit the price increase of each commodity? Can exceed 20% of the purchase price. If the store wants to earn 400 yuan, what should be the price of each commodity? Need? How many pieces have been sold?

Answer: 1.m ≤ 1 and m ≠ 0;

2.

The question means: x 1x2= = 1,

The solution is a = 2.

δ& lt When a=2, δ

∴ only take a =-2;

3. The question means: x 1+x2=9-m2=0.

The solution is m = 3.

When m=3, δ <

∴ only take m =-3, at this time x = 2；;

4.

∫m and n are two of x2-4x+ 1=0,

∴m+n=4, and

M2-4m+ 1=0, that is, m2= 1-4m,

N2-4n+ 1=0, that is, n2= 1-4n,

∴ Original formula = 2 (4m-1)+4 (4n-1)-8n+1.

=8(m+n)-5=8×4-5=27。

5.

The original equation has two equal real roots,

∴δ=b2-4(a+c)×= 0，

∴b2+c2=a2。

∴δabc is RT Δ with hypotenuse.

6. The root of (x+3) (x-3) = 0 is 3,

The denominator of the original equation is x (x-3)+x (x+3) = k,

Substitute X=3 into the above formula and get k= 18.

Substitute X =-3 into the above formula and get k= 18.

∴k= 18.

7.

The question means that δ = 4a2-4 (b+c) (c-b) = 0.

Simplified to a2+b2=c2,

∴∠C=900，

∵

∴m=5 or m =-3.

When m=5, δ <

∴m=-3，

∴ab=m2+3= 12，

Let the height on the hypotenuse be h, then ch=ab,

∴h=。

8.

solve an equation

∫ The sum of length, width and a is less than 2 times of diagonal b,

∴ just take a=7, b=5,

Let x be the length and y the width, then x+y=7, x2+y2=52,

∴x2+2xy+y2=49，

∴25+2xy=49，

∴S=xy= 12.

9. If it takes X days for B to finish alone, then A needs (x-4) days.

Judging from the meaning of the question:

X=2 or x=24,

But when x=2, x-4

∴ Just take x=24, at this time, x-4 = 20,

It takes 24 days to complete B and 20 days to complete A. 。

10.

∵ Earn (A-2 1) yuan per piece, sell (350- 10a) pieces and earn 400 yuan.

∴(a-2 1)(350- 10a)=400，

The solution is a=3 1 or a=25.

∫ The maximum price increase per piece is 2 1× 20% = 4. 1 yuan.

Namely a-2 1 ≤ 4. 1,

∴ Just take a=25, at this time, 350- 10a = 100,

∴: The price of each one is 25 yuan, so we need to sell 100.

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