Question

if p and q are the roots of the equation X square - 2 x minus 1 is equals to zero find the quadratic equation in X whose roots are p + q whole square and p minus q whole square​

Answer 1

Solution :-

Given, p and q be the roots of the equation

x

2

−2x+A=0. So,

p+q=22.....(1)

pq=A...(2)

And, r and s be the roots of the equation

x

2

−18+B=0. So,

r+s=18...(3)

rs=B...(4)

Now, p,q,r and s are in A.P

so let, p=a,q=a+d,r=a+2d,s=a+3d

Now, put these values in equation (1) and (3), we have

a+a+d=2⇒2a+d=2...(5)

And,

a+2a+a+3d=18⇒2a+5d=18...(6)

solving equation (5) and (6),

a=−1, d=4

so p=−1,q=−1+4=3,r=−1+8,s=−1+12=11

Thus,

A=pq=−1×3=−3

B=rs=7×11=77

Then A+B=−3+77=74