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If one root of the quadratic equation ax² + bx + c = 0 is the reciprocal of the other, then which of the following is correct?
Question

If one root of the quadratic equation ax² + bx + c = 0 is the reciprocal of the other, then which of the following is correct?

A.

a = c

B.

ac = 1

C.

b = c 

D.

a = b

Correct option is A

Given:
Equation: ax² + bx + c = 0
Let roots be α and 1/α
Formula used:
For quadratic ax² + bx + c = 0,
Sum of roots = −b/a and Product of roots = c/a
Solution:
α × (1/α) = 1
Therefore, Product of roots = 1
But Product of roots = c/a
So, c/a = 1
=> a = c
Correct answer is (a) a = c

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