Question

Find the exact roots of the polynomial; write the roots in simplest radical form, if necessary.

f(x)=7x^3-11x^2-10x+8

My professor mentioned that the roots are: 2, 1 and 4/7. But I don't know she came up with 4/7. Please help me.

Answer 1

I can see that 2 is a root but not 1?  So I tried -1 by substitution and that works.

So to work out the 3rd root we just use the sum and product of roots theorem.

We have the sum of the roots  = 11/7 and from there the third root is 4/7