Question

The roots of the equation ax² + bx + c = 0 will be reciprocal if 

A) a = bc 

B) b = c 

C) a = b 

D) c = a

Answer 1

Correct option is (D) c = a

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

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

\(\Rightarrow\) \(\alpha\times\frac1\alpha\) \(=\frac ca\)

\(\Rightarrow\) 1 \(=\frac ca\)

\(\Rightarrow\) a = c

Hence, roots of equation \(ax^2+bx+c=0\) will be reciprocal if c = a.

Answer 2

Correct option is D) c = a