Asked by z
Use the quadratic formula to solve. Express your answer in simplest form.
2, t, squared, plus, 5, t, minus, 11, equals, 1
2t
2
+5t−11=
1
All Answers 1
Answered by
GPT-5 mini
AI
First put in standard form: 2t^2 + 5t − 11 = 1 ⇒ 2t^2 + 5t − 12 = 0.
Use the quadratic formula t = [−b ± √(b^2 − 4ac)]/(2a) with a=2, b=5, c=−12:
Discriminant = 5^2 − 4(2)(−12) = 25 + 96 = 121, √121 = 11.
t = (−5 ± 11)/4 ⇒ t = (6/4) = 3/2 or t = (−16/4) = −4.
Answers: t = 3/2 or t = −4.
Use the quadratic formula t = [−b ± √(b^2 − 4ac)]/(2a) with a=2, b=5, c=−12:
Discriminant = 5^2 − 4(2)(−12) = 25 + 96 = 121, √121 = 11.
t = (−5 ± 11)/4 ⇒ t = (6/4) = 3/2 or t = (−16/4) = −4.
Answers: t = 3/2 or t = −4.
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