Question

If alpha,beta are the roots of ax? + bx + c = 0, then find the equation whose roots are (2+alpha) and (2+beta).​

Answer 1

Answer:

α,β are the roots of ⇒ax

2

+bx+c=0

Then, a(α)

2

+b(α)+c=0

Now, α+2=x

Hence, α=x−2

Thus, replace α by x−2 in the given equation,

Required equation is

a(x−2)

2

+b(x−2)+c=0

⇒a(x

2

−4x+4)+bx−2b+c=0

⇒ax

2

+(b−4a)x+(4a−2b+c)=0

⇒ax

2

+x(b−4a)+4a−2b+c=0