Question

What is the condition that one root of the quadratic equation ax² + bx + c=0 is reciprocal of the other ? 

A) a = b 

B) b = c 

C) a = c 

D) a + b + c = 0

Answer 1

Correct option is (C) a = c

Let \(\alpha\;and\;\frac1\alpha\) be roots of equation \(ax^2+bx+c=0.\)

\(\therefore\) Product of roots \(=\frac ca\)

\(\Rightarrow\frac ca=\alpha.\frac1\alpha=1\)

\(\Rightarrow\) c = a

Hence, the condition that one root of the quadratic equation \(ax^2+bx+c=0\) is reciprocal of the other is a = c.

Answer 2

Correct option is C) a = c