Question

If the roots of the equation x 2 + p x +q =0 differ by 2 find the relation between p & q

Answer 1

Answer:

Let a and b be two roots

a+b=p and a.b=q and a-b=2

(a+b)+(a-b)=p+2

2a=p+2, a=(p+2)/2

(a+b)-(a-b)=p-2

2b=(p-2)

b=(p-2)/2

a×b=q

(p+2)×(p-2)/4=q

p^2-4=4q

p^2-4q-4=0 Ans