Question

Determine all of the roots of 4x^3-4x^2-11x+6=0 if 2 is known to be one of the roots.

Answer 1

Hint: If 2 is one of the roots, then (x-2) must be one of the factors. Use long division or synthetic division to find the other factors

Answer 2

ok thanks

Answer 3

so I get 4x^2+4x-3 with no remainder, do I break that down and take the factoprs and those become the roots?

Answer 4

4x^2+4x - 3
4x^2+6x -2x - 3
2x(2x+3)-1(2x +3)
(2x+3)(2x-1)

Does that help?

Answer 5

So now check by multiplying

(x-2)(2x+3)(2x-1)

Answer 6

ok so I set each of those equal to 0 to find the roots. Thanks!