Question

if alpha and 1/alpha are the zeroes of polynomial ax2+bx+c then find the value of c​

Answer 1

Answer:

c=a

Step-by-step explanation:

we know that product of roots = c/a

-> alpha * 1/alpha = c/a

alpha and 1/alpha got cancelled,

-> 1 = c/a

So, c=a

Hope it helps you!!

Answer 2

Given:

A quadratic polynomial ax2+bx+c having two zeroes alpha and 1/alpha.

To find:

The value of c.

Solution:

As we know that, in a quadratic polynomial ax2+bx+c having two zeroes alpha and beta, the product of alpha and beta is equal to:

$\frac{c}{a}$

So, as given, the two zeroes of the given polynomial ax2+bx+c are alpha and 1/alpha. So, we have

$\alpha \times \frac{1}{ \alpha } = \frac{c}{a}$

On solving above, we have

$\frac{c}{a} = 1$

$c = a$

So, the value of c is equal to a.

Hence, the value of c is a.