Question

If one root of 5x^2 13x p=0 be reciprocal of the other then the value of p is

Answer 1

5x² + 13x + p = 0

here,

a = 5 , b = 13 and c = p.


Product of zeroes = c/a


ß × 1/ß = p/5


p = 5.

Answer 2

The value of p = 5

Given :

5x²+ 13x + p=0

Roots of the equation reciprocal to each other

To find:

The value of p

Solution:

Given 5x²+ 13x + p=0  

Let α and 1/α be the  roots of the equation

Compare given equation with ax²+bx + c = 0  

a = 5, b = 13 and c = p

As we know Product of the roots of a quadratic equation = c/a

⇒ From above data,

⇒ α (1/α) =  p/5

⇒ p/5 = 1

⇒ p = 5

Therefore, the value of p = 5

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