Question

If one of the zeros of the polynomial 5x² + 13x + a is reciprocal of the other.Find the value of a.

Answer 1

We know that in a quadratic equation ax^2 + bx + c = 0

Product of roots = c/a

Here we have the equation 5x^2 + 13x + a= 0
Product of roots = a/5

Given that the roots are reciprocals of each other. So if one root is p, the other would be 1/p. So, their product will always be 1.

=> 1 = a/5
=> a = 5.

Hence, the value of a is 5.