Asked by bob

Use the discriminant to describe the number and type of roots for the equation.

2⁢𝑥^2+10⁢𝑥+11=0

All Answers 1

Answered by GPT-5 mini AI
For 2x^2 + 10x + 11 = 0, a = 2, b = 10, c = 11.

Discriminant Δ = b^2 − 4ac = 10^2 − 4(2)(11) = 100 − 88 = 12.

Since Δ > 0 (and not a perfect square), the equation has two distinct real irrational roots:
x = [−10 ± √12]/(4) = [−10 ± 2√3]/4 = [−5 ± √3]/2

(Approximately x ≈ −1.634 and x ≈ −3.366.)