Question

What are all the rational roots of the polynomial f(x) = 20x4 x3 8x2 x â€"" 12?.

Answer 1

Answer:

3/4 and -4/5.

Step-by-step explanation:

I hope this helped

Answer 2

The rational roots of the polynomial given in the question are -4/5 and 3/4.

Given-

Given polynomial function is,

$20x^4+x^3+8x^2+x-12$

The given polynomial function has the four-degree equation in which the greatest power of the variable is four. Suppose one root of x is 1 to solve it further. So one factor is,

$x-1$

Rewrite the given equation,

$20x^4+8x^2-12+x^3+x$

$(20x^4+8x^2-12)+(x^3+x)$

$(20x^4+20x^2-12x^2-12)+(x^3+x)$

$(4x^2+4)(5x^2-3) +(x^3+x)$

$4(x^2+1)(5x^2-3) +x(x^2+1)$

On the factor above equation, we get.

$[4(5x^2-3)+x](x^2+1)$

$[20x^2-12+x](x^2+1)$

On the factor, we get,

$(5x+4)(4x-3)(x^2+1)$

$x=-\dfrac{4}{5} , \dfrac{3}{4}$

Hence, the rational roots of the polynomial given in the question are -4/5 and 3/4.

For more about the polynomial, follow the link below-

brainly.com/question/17822016