Asked by bob
Use the discriminant to describe the number and type of roots for the equation.
2𝑥^2+10𝑥+11=0
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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.)
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.)
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