Question

which statement about the following equation is true?

(2x^2 - 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

Explanation:

Rewrite the quadratic equation in standard form

$$
LATEXBLOCK0
$$

Calculate the discriminant

$$
LATEXBLOCK1
$$

Determine the nature of the roots

$$
LATEXBLOCK2
$$

Answer:

• 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 (Correct answer)
• The discriminant is greater than 0, so there are two complex roots