Question

1. Consider the quadratic equation 3x2 – 7 = 5x.

(a) What is the value of the discriminant?
(b) What does the discriminant of the quadratic equation tell about the solutions to 3x2 – 7 = 5x?

Answer 1

a) 109

b) The quadratic has two distinct, real, roots.

Explanation:

First, rearrange the quadratic so that it is in the form ax²+bx+c to get 3x²-5x-7.

The value of the discriminant of a quadratic ax²+bx+c is b²-4ac, which in this case is (-5)² - 4(3)(-7) = 25+84=109.

Because the value of the discriminant is positive, this tells us that the quadratic has two distinct, real, roots.