Answer:
-0.8 and 0.75.
Step-by-step explanation:
20x^4 + x^3 + 8x^2 + x – 12 = 0
by the rational roots theorem:-
The leading coefficient is 20 with factors +/- 1,2,4,5,10,20
and the constant is -12 with factors +/- 1,2,3,4,6,12
so there are many possible roots like -1, 2, 3/4 3/5 , -4/5 .....
Drawing a graph would be the quickest way to do this, either manually, using graphical software or a graphical calculator.
I used the latter and got 2 rational roots -0.8 and 0.75.
The rational roots of the polynomial f(x) = 20[tex]x^4[/tex] + [tex]x^3[/tex] + 8[tex]x^2[/tex] + x – 12 is -0.8 and 0.75 and this can be determined by sketching the graph of the given polynomial.
Given :
f(x) = 20[tex]x^4[/tex] + [tex]x^3[/tex] + 8[tex]x^2[/tex] + x – 12
The following steps can be used in order to determine the rational roots of the given polynomial:
Step 1 - Write the polynomial equation.
f(x) = 20[tex]x^4[/tex] + [tex]x^3[/tex] + 8[tex]x^2[/tex] + x – 12
Step 2 - Draw the graph of the above polynomial equation.
Step 3 - The coefficient of [tex]x^4[/tex] is 20 with factors +/- 1,2,4,5,10,20
Step 4 - The constant term of the given polynomial is -12 with factors +/- 1,2,3,4,6,12.
Step 5 - So, from the polynomial equation, the two rational roots are -0.8 and 0.75.
For more information, refer to the link given below:
https://brainly.com/question/3655826
