Question

The roots of the equation ax2 + bx + c =0 will be reciprocal of each other if
(a) a=b
(b) c=a
(c) b=c
(d) b=0

Answer 1

Let k be one of the root of the given equation. According to the problem, 1/k will be the other root of the given equation. We know that, product of the roots of the equation = c/a. Therefore, k × 1/k = c/a. or, 1 = c/a. or, a = c [multiplying a on both sides]. The roots of the equation ax2 + bx + c = 0 will be reciprocal if a = c. Therefore, a = c or c = a. Answer: (b)