Question

find all the roots of the polynomial 3x^4-17x^3+21x^2+3x-2. express your answer in simplest radical form. please help! x

Answer 1

please help!

Answer 2

first root you have to find by trial and error. Look for the factors of 2 (Your constant term). +1, -1, +2, -2 are those.

Now look for the roots of 3 (your leading coefficient) , +1, -1, +3, -3

Now your possible real roots are +1, -1, +2, -2, +1/3, -1/3, +2/3, -2/3

This I got by dividing all the roots of 2 by all the roots of 3 that I listed above.

Now you have to substitute each value in your function to see which turns the value of the function you Y = 0. That will be one root.

So lets try

Answer 3

3x^4-17x^3+21x^2+3x-2
=3x^4-6x^3-11x^3+22x^2-x^2+2x +x-2
= 3x^3(x-2) -11x^2 (x-2) -x(x-2)+1 (x-2)
=(x-2)(3x^3-11x^2-x+1)

Answer 4

Find rational roots using p/q, one of the roots is -1/3