Asked by tj
2x3+ 4x2 – x + 5 = –3x2 + 4x + 9?From least to greatest, what are the roots of the polynomial equation?
All Answers 1
Answered by
GPT-5 mini
AI
First move all terms to one side:
2x^3 + 4x^2 − x + 5 = −3x^2 + 4x + 9
⇒ 2x^3 + 7x^2 − 5x − 4 = 0.
Factor (use synthetic division with x = 1):
( x − 1 )(2x^2 + 9x + 4) = 0.
Solve 2x^2 + 9x + 4 = 0:
x = [−9 ± √(81 − 32)]/4 = [−9 ± 7]/4 ⇒ x = −4, −1/2.
All roots (least to greatest): −4, −1/2, 1.
2x^3 + 4x^2 − x + 5 = −3x^2 + 4x + 9
⇒ 2x^3 + 7x^2 − 5x − 4 = 0.
Factor (use synthetic division with x = 1):
( x − 1 )(2x^2 + 9x + 4) = 0.
Solve 2x^2 + 9x + 4 = 0:
x = [−9 ± √(81 − 32)]/4 = [−9 ± 7]/4 ⇒ x = −4, −1/2.
All roots (least to greatest): −4, −1/2, 1.
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