Question

What are the approximate values of the non-integral roots of the polynomial equation? x4 − 4x3 = 6x2 − 12x

Answer 1

1.27

4.73

Explanation:

Answer 2

x ≈ 3.28547335182

Explanation:

We assume your polynomial is supposed to be ...

`x^4-4x^3+6x^2-12x`

The only integral root is x=0.

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The approximate value of the non-integral root can be found by graphing to be 3.285. This value can be refined using Newton's Method iteration to give ...

x ≈ 3.28547335182 . . . . approximate non-integer real root

Dividing the known real roots from the quartic gives a quadratic function with a vertex at approximately (0.357, 3.525). Then the complex roots are approximately ...

0.357 ± i√3.525 . . . . approximate complex roots