Question

Y = x^3 - 52x^2 + 15x^4 + 16 + 20x

Answer 1

The factors of the equation of power 4, $y=x^{3}-52x^{2} +15x^{4} +16+20x$  are x=1, -2, 4/3, -2/5.

Given equation is $y=x^{3}-52x^{2} +15x^{4} +16+20x$,

By performing L-division method, we get

$y = (x-1)(15x^{3} +16x^{2} -36x-16)$

Then again doing the same L-division method to the cubic equation $15x^{3} +16x^{2} -36x-16$, we get

$15x^{3} +16x^{2} -36x-16 = (x+2)(15x^{2} -14x-8)$

Therefore, $y = (x-1)(x+2)(15x^{2}-14x-8)$

Then finally the roots of the quadratic equation $15x^{2}-14x-8$ are (x-(4/3)) and (x+(2/5))

Hence, $y=x^{3}-52x^{2} +15x^{4} +16+20x = (x-1)(x+2)(x-\frac{4}{3} )(x+\frac{2}{5} )$

Therefore, the roots of the equation of power 4, $y=x^{3}-52x^{2} +15x^{4} +16+20x$ are x=1, -2, 4/3, -2/5.

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