Question

If the roots of ax² + bx -3 =0 are reciprocal of each other then :

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Answer 1

Let the roots of the equation ax2 + bx + c = 0 are α and 1 α . (∵ Given that roots of equation are reciprocal to each other.) Hence, if a = c then the roots of equation ax2 + bx + c = 0 are reciprocal to each other.

Answer 2

SOLUTION

TO DETERMINE

If the roots of ax² + bx - 3 = 0 are reciprocal of each other then

EVALUATION

Here the given Quadratic equation is

ax² + bx - 3 = 0

Now it is given that the roots are reciprocal of each other

Let the roots are α and 1/α

Now

Product of the zeroes = c/a

⇒ α × 1/α = - 3/a

⇒ 1 = - 3/a

⇒- 3/a = 1

⇒a = - 3

FINAL ANSWER

If the roots of ax² + bx - 3 = 0 are reciprocal of each other then a = - 3

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