Question

1)x^2+9x+14=0 2)2x^2-23x+65=0 3)2x^2-27x+88=0 4)x^2-5x+6=0 5)x^2-14x+49=0 6)x^2-9x+14=0 7)x^2+4x=0 8)3x^2-9=0 9)4x^2-8=0 10)x^2-6x=0

Answer 1

5. D=(-14)^2-4×1×49=0

x1,x2= 7

6. D=(-9)^2-4×1×14=25

x1=7 x2= 2

7. x(x+4)=0

x=0 x=-4

8. 3(x^2-3)=0

x=+-√3

9. 4(x^2-2)=0

x=+-√2

10. x(x-6)=0

x=0 x=6

Answer 2

It looks like you have provided a list of quadratic equations, and it seems you might be interested in solving them for their solutions (roots). I can certainly help you with that. Let's solve each of these quadratic equations one by one:

1. x^2 + 9x + 14 = 0 This quadratic equation can be factored as (x + 7)(x + 2) = 0. So, the solutions are x = -7 and x = -2.

2. 2x^2 - 23x + 65 = 0 This equation can be factored as (2x - 13)(x - 5) = 0. The solutions are x = 13/2 and x = 5.

3. 2x^2 - 27x + 88 = 0 Factoring this equation gives (2x - 11)(x - 8) = 0. The solutions are x = 11/2 and x = 8.

4. x^2 - 5x + 6 = 0 Factoring this equation gives (x - 2)(x - 3) = 0. The solutions are x = 2 and x = 3.

5. x^2 - 14x + 49 = 0 This equation is a perfect square trinomial, (x - 7)^2 = 0. The only solution is x = 7.

6. x^2 - 9x + 14 = 0 Factoring this equation gives (x - 7)(x - 2) = 0. The solutions are x = 7 and x = 2.

7. x^2 + 4x = 0 Factoring out x gives x(x + 4) = 0. The solutions are x = 0 and x = -4.

8. 3x^2 - 9 = 0 This equation can be factored as 3(x - 1)(x + 1) = 0. The solutions are x = 1 and x = -1.

9. 4x^2 - 8 = 0 Factoring out 4 gives 4(x^2 - 2) = 0. The solutions are x = √2 and x = -√2.

10. x^2 - 6x = 0 Factoring out x gives x(x - 6) = 0. The solutions are x = 0 and x = 6.

These are the solutions for the given quadratic equations. If you have any further questions or need more explanation, feel free to ask!