Question

If ‘alpha’ and ‘beta’ are the zeroes of the quadratic polynomial f(x) = 3x2-5x-2,then evaluate alpha^3*beta + beta^3alpha

Answer 1

Dear Student,
$$\begin{gathered} f\left(x\right)=3x^2-6x+x-2=0 \\ =3x(x-2)+1(x-2)=0 \\ (3x+1)(x-2)=0 \\ Hencezeroesare-1/3and2 \\ let\alpha =-1/3and\beta =2 \\ {\alpha }^3+{\beta }^3=\frac{-1}{27}+8 \\ =\frac{215}{27} \end{gathered}$$

Regards!