Question

Describe the solutions to y-6x^2-5x+6
A. 2 imaginary solutions
B. 3 real solutions
C. 1 real & 1 imaginary solution
D. 2 real solutions

Answer 1

6x^2 - 5x = 6
==> 6x^2 - 5x - 6 = 0

The solutions of ax^2 + bx + c = 0 are given by:

x = [-b +/- √(b^2 - 4ac)] / 2a

In this case, a = 6, b = -5, and c = -6.

x = [-b +/- √(b^2 - 4ac)] / 2a
==> x = {-(-5) +/- √[(-5)^2 - 4*6*(-6)]} / (2*6)
==> x = {5 +/- √[25 - (-144)]} / 12
==> x = (5 +/- √169) / 12
==> x = (5 +/- 13) / 12

x = (5 + 13) / 12
==> x = 18 / 12 -> x = 1.5

x = (5 - 13) / 12
==> x = -8 / 12 -> x = -2/3