Question

if alpha and beta ar3 the zeroes of the polynomial f(x)=5x²-7x+1,then find the value of (alpha/beta+beta/alpha​

Answer 1

Sum of zeroes,

$\alpha +\beta = \frac{-b}{a} = \frac{7}{5}$

Product of zeroes,

$\alpha \beta = \frac{c}{a} =\frac{1}{5}$

We need to find

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

Take LCM and make denominator common

$= \frac{\alpha^2+\beta ^2 }{\alpha\beta }$

= $\frac{(\alpha+\beta)^2 - 2\alpha \beta }{\alpha \beta }$

Substitute known values

$= \frac{(7/5)^2-2*(1/5)}{(1/5)}$

$= \frac{7^2+10}{5}$

$= \frac{59}{5}$

SO THE ANSWER IS 59/5