Quadratic equations ( maths )

Question

It is given that h and k are the roots of the quadratic equation ( x+3 ) ( x-2 ) = 6, where h > k. Find the possible values of k.

Answer 1

(x+3)(x-2) = 6

x^2 +x -6 = 6

x^2 +x -12 = 0

x^2 +x + 1/4 -12 -1/4 = 0

(x+1/2)^2 - 49/4 = 0

the vertex of the upward opening parabola is (-1/2, -49/4)

x^2 +x -12 = 0

(x-3)(x+4) = 0

x = 3 or -4

h=3, k=-4 are the two roots, with h>k