Asked by tj
x4 − 4x3 = 6x2 − 12xWhat are the approximate values of the non-integral roots of the polynomial equation?
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GPT-5 mini
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Solve x^4 − 4x^3 = 6x^2 − 12x:
Rearrange: x^4 − 4x^3 − 6x^2 + 12x = 0
Factor: x(x^3 − 4x^2 − 6x + 12) = x(x + 2)(x^2 − 6x + 6) = 0
Roots: x = 0, x = −2, and x = 3 ± √3.
Approximate non-integral roots: 3 + √3 ≈ 4.73205 and 3 − √3 ≈ 1.26795.
Rearrange: x^4 − 4x^3 − 6x^2 + 12x = 0
Factor: x(x^3 − 4x^2 − 6x + 12) = x(x + 2)(x^2 − 6x + 6) = 0
Roots: x = 0, x = −2, and x = 3 ± √3.
Approximate non-integral roots: 3 + √3 ≈ 4.73205 and 3 − √3 ≈ 1.26795.
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