Question

If one zero of the polynomial 5x2 + 13x - p is reciprocal of the other, then find p

Answer 1

Let the zeroes be a and b
Also, b=1/a

a.b= -p/5
i.e. a.1/a= -p/5
Therefore,
p= -5

Answer 2

Answer:

The value of p is -5.

Step-by-step explanation:

Given : If one zero of the polynomial $5x^2 + 13x - p$ is reciprocal of the other.

To find : The value of p?

Solution :

Let one of the zero of the polynomial is $\alpha$

Other zero of the polynomial is  $\frac{1}{\alpha}$

We have given a quadratic equation $p(x)=5x^2 + 13x - p$

The zero of the polynomial $f(x)=ax^2+bx+c$

$\alpha +\beta =-\frac{b}{a}$

Substitute the value,

$\alpha +\frac{1}{\alpha}=-\frac{13}{5}$

$\alpha \times\beta =\frac{c}{a}$

Substitute the value,

$\alpha\times \frac{1}{\alpha}=\frac{-p}{5}$

$1=\frac{-p}{5}$

$p=-5$

The value of p is -5.