Question

Find the quadratic polynomial whese Zeros are sresiprocals of the zeros of the polynomial f(x) = ax² + bx +c. C is not equal to zero​

Answer 1

Explanation:

Find the quadratic polynomial whese Zeros are sresiprocals of the zeros of the polynomial f(x) = ax² + bx +c. C is not equal to zeroLet p,q be zeros of ax

2

+bx+c

∴p+q=

a

−b

& pq=

a

c

Let P & Q be zeros of required polynomial

It is given that P= 1/p , Q=1/q

Then,

P+Q=

p

1

+

q

1

=

pq

q+p

=

c/a

−b/a

=

c

−b

PQ=

p

1

.

q

1

=

pq

1

=

c

a

∴ Required polynomial = x

2

+

c

b

x+

c

a

⇒cx

2

+bx+a