Question

if alpha,beta are the zeroes of the quadratic polynomial f(x)=x²-px+q, then prove that 1/alpha +1/beta=p/q​

Answer 1

Answer:

$f(x)= {x}^{2}-px+q$

let the coefficients be a, b, c.

a=1. ,b=-p,. c=q

We know the relation between coefficients and zeros of the quadratic polynomial,i.e.,

• ${α+β} = \frac{-b}{a}$

• ${α}{β} = \frac{c}{a}$

= let solve L.H.S.

$\frac{1}{α} + \frac{1}{β}$

$\frac{α+β}{αβ}$

= on putting the value,

$\frac{p}{q}$

R.H.S.= $\frac{p}{q}$

hence proved....

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