Question

If a and b are zeroes of the polynomial 3x^2-3x-5. find a^3+b^3​

Answer 1

We are given the following polynomial.

$3x^2-3x-5=0$

and a and b are it's roots.

We need to find $a^3+b^3$.

using a and b relation, we get

$a+b=\frac{3}{3} =1$  --------1

$ab=\frac{-5}{3}$ --------2

Now,

$a^3+b^3=(a+b)^3-3ab(a+b)$

          $=(1)^3-3(\frac{-5}{3} )(1)$

         $=1-(-5)\\=1+5=6$

∴ $a^3+b^3=6$