Question

Which statement about the following equation is true?

2x2 – 9x + 2 = –1
The discriminant is less than 0, so there are two real roots.
The discriminant is less than 0, so there are two complex roots.
The discriminant is greater than 0, so there are two real roots.
The discriminant is greater than 0, so there are two complex roots.

Answer 1

First rewrite: 2x^2 − 9x + 2 = −1 ⇒ 2x^2 − 9x + 3 = 0.

Discriminant D = b^2 − 4ac = (−9)^2 − 4(2)(3) = 81 − 24 = 57, which is > 0.

So the correct statement is: "The discriminant is greater than 0, so there are two real roots."