Answer:
3/4 and -4/5.
Step-by-step explanation:
I hope this helped
The rational roots of the polynomial given in the question are -4/5 and 3/4.
Given-
Given polynomial function is,
[tex]20x^4+x^3+8x^2+x-12[/tex]
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,
[tex]x-1[/tex]
Rewrite the given equation,
[tex]20x^4+8x^2-12+x^3+x[/tex]
[tex](20x^4+8x^2-12)+(x^3+x)[/tex]
[tex](20x^4+20x^2-12x^2-12)+(x^3+x)[/tex]
[tex](4x^2+4)(5x^2-3) +(x^3+x)[/tex]
[tex]4(x^2+1)(5x^2-3) +x(x^2+1)[/tex]
On the factor above equation, we get.
[tex][4(5x^2-3)+x](x^2+1)[/tex]
[tex][20x^2-12+x](x^2+1)[/tex]
On the factor, we get,
[tex](5x+4)(4x-3)(x^2+1)[/tex]
[tex]x=-\dfrac{4}{5} , \dfrac{3}{4}[/tex]
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-
https://brainly.com/question/17822016
