Question

If α&β are zeroes of a quadratic polynomial x-px+q=0 then find 1/α+1/β

Answer 1

1/α + 1/β
= (α+β)/αβ
For an equation ax²+bx+c=0
α+β= -b/a
αβ= c/a
Given equation is x²-px+q
a=1 b=-p c=q
Substituting values
(p/1)/(q/1)
=p/q

Answer 2

Heya !!!


here is your answer!!!


x² - px + q = 0




$\alpha \: and \: \beta \: are \: \: the \: zeroes$


sum of zeros = p



Product of zeroes = q


now ,


=> 1 / alpha + 1 / ß

=> alpha + beta / alpha *ß



=> p /q


hence ,



$1 \div \alpha + 1 \div \beta$
=> p / q



hope it helps you dear !!!

thanks !!!