Question

Find a quadratic polynomial, whose zeroes are reciprocals of the zeroes of the polynomial
$x ^{2} - x - 6$
​

Answer 1

Answer:

Find the quadratic polynomial whose zeros are reciprocals of the zeros of the polynomials f(x)=ax  

2

+bx+c, a



=0, c



=0.

Answer

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

 

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Answer 2

Answer:

bala bala bla sathan ka sala bala bala bala