Question

If $2,2$ are the roots of $x^2+px+b=0$ and $1,4$ are the roots of $x^2+ax+q=0$, then roots of the equation $x^2+ax+b=0$ are

• A. real and distinct
• B. imaginary
• C. real and equal
• D. irrational

Answer 1

The correct option is A real and distinct

First equation :

-p=4$\Rightarrow$p=-4 and b=4(applying sum and product of roots)

Second equation :

$a=-5$ and $q=4$

Third equation :

$\Rightarrow x^2-5x+4=0$

$\Rightarrow (x-4)(x-1)=0$

$\therefore$x=4,1

$\Rightarrow$real and distinct roots