Question

If alpha and beta are the roots of the equation 3x2 -2x- 1=0.
Find 1. Alpha - beta
2. Apha cubed - beta cubed

Answer 1

Roots of this equation are $1$ and $-\frac{1}{3}$

1.Alpha - beta is equal $\pm(1-(-\frac{1}{3}))=\pm\frac{4}{3}$

2.Apha cubed - beta cubed is equal $\pm(1^3-(-\frac{1}{3})^3)=\pm(1+\frac{1}{27})=\pm\frac{28}{27}$

Ansswer: 1) $\pm\frac{4}{3}$ , 2) $\pm\frac{28}{27}.$