Question

Find a quadratic polynomial whose zeroes are
reciprocals of the zeroes of the polynomial
f(x) = ax^2+ bx + C, a not equal to 0, C not equal to 0. [CBSE 2020]​

Answer 1

Answer:

Required polynomial = x

2

+

c

b

x+

c

a

⇒cx

2

+bx+a

Step-by-step explanation:

Let 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