Question

What are the roots of the polynomial equation x superscript 4 baseline x squared = 4 x cubed minus 12 x 12? use a graphing calculator and a system of equations. round noninteger roots to the nearest hundredth. –12, 20 –2.73, 2, 2.73 –1.73, 1.73, 2 –20, 12

Answer 1

The roots of the provided polynomial equation of 4 degree are 2,2,1.73,-1.73.

What is a factor of polynomial?

The factor of a polynomial is the terms in linear form, which are, when multiplied together, give the original polynomial equation as a result.\

To find the roots of a polynomial, equate these factors of a polynomial to zero.

The given polynomial equation is,

$x^4+x^2=4x^3-12x+12$

Take all the terms left side of the equation,

$x^4+x^2-4x^3+12x-12=0\\x^4-4x^3+x^2+12x-12=0$

The factor form of the polynomial on solving the above equation, we get,

$(x-2)(x-2)(x-1.73)(x+1.73)=0$

Equate all the factors to zero, to find the roots. The roots we get are,

$2,2,1.73,-1.73$

Hence, the roots of the provided polynomial equation of 4 degree are 2,2,1.73,-1.73.

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