Question

The sum of the reciprocals of the roots of the equation x² + px + q = 0 is

A) q/p

B) p/q

C) -q/p

D) -p/q

Answer 1

Correct option is (D) -p/q

Let \(\alpha\;and\;\beta\) are roots of equation \(x^2+px+q=0.\)

\(\therefore\) Sum of roots \(=\frac{-p}1=-p\)

\(\Rightarrow\) \(\alpha+\beta\) = -p    ______________(1)

& Product of roots \(=\frac{q}1=q\)

\(\Rightarrow\) \(\alpha\beta\) = q         ______________(2)

Now, \(\frac1\alpha+\frac1\beta=\frac{\alpha+\beta}{\alpha\beta}\) \(=\frac{-p}{q}\)

Hence, the sum of reciprocals of the roots of given equation is \(\frac{-p}{q}.\)

Answer 2

Correct option is D) -p/q