Question

If $\alpha$ and $\beta$ are the zeroes of the polynomial $f\left(x\right)=6x^2+x-7$ then evaluate the following:

(i)$\alpha -\beta$ (ii)${\alpha }^2+{\beta }^2$ (iii) ${\alpha }^2-{\beta }^2$ (iv) ${\alpha }^3-{\beta }^3$ (v) ${\alpha }^3+{\beta }^3$ (vi) ${\alpha }^4-{\beta }^4$

Answer 1

Zeroes are $-\frac{7}{6},1$

1) $-\frac{13}{7}$

2) $\frac{85}{49}$

3) $\frac{13}{49}$

4) $\frac{127}{343}$

5) $\frac{559}{343}$

6) $\frac{1105}{2401}$