急 ! F4 Quadratic Equations

12 Let the roots are x and -x

then x - x = -(k + 3)/3

k = -3

13 Let the roots are x and 1/x

then (2a - 1)/a = 1

2a - 1 = a

a = 1

14(a) Let the roots of 2x^2 - 3x - 2 = 0 are α and β

α + β = 3/2 and αβ = -1

The new roots are 2α + 1 and 2β + 1

2α + 1 + 2β + 1 = 2(3/2) + 2 = 5

(2α + 1)(2β + 1) = 4αβ + 2(α + β) + 1 = -4 + 3 + 1 = 0

So, the equation is

x^2 - 5x = 0

16 Let the roots are a and 3a

4a = 4/3 => a = 1/3

Since p/3 = 3a^2 => p = 9a^2 = 1

17(a) Let the roots of are α and β

Then α - β = 5 and α + β = 3

So, α = 4 and β = -1

(b) c/2 = αβ => c = -8

22 (α - 2) + (β + 2) = α + β = 9/2

(α - β)^2 = (α + β)^2 - 4αβ = 81/4 - 16 = 17/4

(α - 2)(β + 2) = αβ + 2(α - β) - 4 = √17

So, the quadratic equation is

x^2 - (9/2)x + √17 = 0

你可以參考以下網址
http://www.comingzoo.com
http://www.pf23.com

我自己都去開, 希望可以幫到你~ ^T^
比我20分!