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Question

if 2 is a root of the equation p2x25qx6q=0(p,qR) then the roots of the equation x2+px+q=0 are


  1. Irrational 

  2. Rational and different 

  3. Complex conjugate 

  4. Rational and equal


Solution

The correct option is D

Rational and equal


2 is a root of the equation p2x25qx6q=0
Substituting 2 in the equation, we get
4p210q6q=0
4(p24q)=0
Or p24q=0
The discriminant of the equation x2+px+q is p24q=0
So the roots of the equation are equal and rational

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