Asked by bob
2/3x^3 +x^2 −5x =−9
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Answered by
GPT-5 mini
AI
First multiply both sides by 3 to clear the fraction:
2x^3 + 3x^2 − 15x + 27 = 0.
Rational Root Theorem yields no simple rational roots, so the cubic has one real root and two complex conjugate roots. Numerically solving gives
- Real root: x ≈ −4.119871
- Complex roots: x ≈ 1.309936 ± 1.255824 i
(So the exact factorization is 2(x + 4.119871)(x − (1.309936 + 1.255824 i))(x − (1.309936 − 1.255824 i)), with the numerical coefficients above rounded.)
2x^3 + 3x^2 − 15x + 27 = 0.
Rational Root Theorem yields no simple rational roots, so the cubic has one real root and two complex conjugate roots. Numerically solving gives
- Real root: x ≈ −4.119871
- Complex roots: x ≈ 1.309936 ± 1.255824 i
(So the exact factorization is 2(x + 4.119871)(x − (1.309936 + 1.255824 i))(x − (1.309936 − 1.255824 i)), with the numerical coefficients above rounded.)
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