Question

show that x^2+px+q=0 and x^2+qx+p=0 have common roots if p=q or p+q+1=0

Answer 1

Answer :

Given equations are

x² + px + q = 0 ...(i)

x² + qx + p = 0 ...(ii)

For common roots, we must have

1/1 = p/q = q/p

⇨ 1/1 = p/q = q/p = (1 + p + q)/(1 + q + p)

⇨ (p + q + 1)/(p + q + 1) = p/q

⇨ p (p + q + 1) - q (p + q + 1) = 0

⇨ (p - q) (p + q + 1) = 0

Either, p - q = 0 or, p + q + 1 = 0

i.e., p = q or, p + q + 1 = 0

Hence, proved.

#MarkAsBrainliest