Question

If alpha and beta are zeroes of p(x)=3x^2 -5x-2, then find (i)1/alpha+1/beta (ii) alpha^2.beta+alpha.beta^2??

Answer 1

I think it's clear that sum of roots=-b/a and product of roots=c/a

Answer 2

Answer:

$\text{The value of }\frac{1}{\alpha}+\frac{1}{\beta}\text{ is }\frac{-5}{2}\text{ and the value of }\alpha^2.\beta+\alpha.\beta^2\text{ is }\frac{-10}{9}$

Step-by-step explanation:

$\text{Given that }\alpha\text{ and }\beta \text{ are the zeroes of the polynomial }3x^2-5x-2$

$\text{we have to find the value of }\frac{1}{\alpha}+\frac{1}{\beta}\text{ and }\alpha^2.\beta+\alpha.\beta^2$

$P(x)=3x^2-5x-2$

$\text{sum of zeroes=}\alpha+\beta=\frac{-b}{a}=\frac{-(-5)}{3}=\frac{5}{3}$

$\text{product of zeroes=}\alpha.\beta=\frac{c}{a}=\frac{-2}{3}$

$\frac{1}{\alpha}+\frac{1}{\beta}$

$\frac{\beta+\alpha}{\alpha.\beta}=\frac{\frac{5}{3}}{\frac{-2}{3}}=\frac{-5}{2}$

$\alpha^2.\beta+\alpha.\beta^2$

$\alpha.\beta(\alpha+\beta)=\frac{-2}{3}\times \frac{5}{3}=\frac{-10}{9}$

$\text{Hence, the value of }\frac{1}{\alpha}+\frac{1}{\beta}\text{ is }\frac{-5}{2}\text{ and the value of }\alpha^2.\beta+\alpha.\beta^2\text{ is }\frac{-10}{9}$