Question

if p and q are the zeroes of a quadratic polynomial where p + q = 24 and p - q = 8 then write the quadratic polynomial​

Answer 1

Answer:

Given, p-q=8

p = 8 + q ----(I)

And p+q= 24

by equation (I) we get,

8+q +q=24

8 + 2q =24

2q=16

q=8

Therefore , p= 8 + 8 =16

So, here , zeroes of the polynomial = 8 and 16

Therefore the required polynomial

= x2 + (8+16)x + (8*16)

=x2 + 24x + 128

Answer 2

Answer:

p(x)=x^2-24x+128

Step-by-step explanation:

p and q are the zeros of a polynomial

Let the polynomial be p(x)

So,p(x)=x^2-(sum of zeros)x+(product of zeros)

We know sum of zeros, we will find product of zeros

p+q=24

Squaring the equation

(p+q)^2=24^2

p^2+q^2+2pq=576

p^2+q^2=576-2pq. .....(1)

p-q=8

Squaring the equation

(p-q)^2=8^2

p^2+q^2-2pq=64

Substituting (1)

576-2pq-2pq=64

4pq=576-64

pq=512/4

pq=128

Now,

p(x)=x^2-(p+q)x+pq

Substituting the values

p(x)=x^2-24x+128