Question

Which statement about the following equation is true?

3x2 – 8x + 5 = 5x2
The discriminant is less than 0, so there are two real roots.
The discriminant is greater 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 complex roots.

Answer 1

First put in standard form: 3x^2 − 8x + 5 = 5x^2 ⇒ −2x^2 − 8x + 5 = 0 ⇒ 2x^2 + 8x − 5 = 0.

Discriminant Δ = b^2 − 4ac = 8^2 − 4(2)(−5) = 64 + 40 = 104 > 0.

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