Question

find h and k such that the equation 3x^2 -hx +4k =0, so that the sum of the solutions is -12 and the product of the solutions is 20.

Answer 1

Let the solutions be a and b.
a = -2; b = -10
a + b = -2 + (-10) = -12
ab = (-2)(-10) = 20

(x - a)(x - b) = 0

(x - (-2))(x - (-10)) = 0

(x + 2)(x + 10) = 0

x^2 + 10x + 2x + 20 = 0

x^2 + 12x + 20 = 0

-h = 12

h = -12

4k = 20

k = 5