Question

The roots of equation $x^2+px+q=0$ are $1$ and $2$ . The roots of the equation $q{x}^2-px+1=0$ must be

• A. $-1,$ $-\frac{1}{2}$
• B. $\frac{1}{2},1$
• C. $-\frac{1}{2},1$
• D. $-1,\frac{1}{2}$

Answer 1

The correct option is A $-1,$ $-\frac{1}{2}$

The equation can be written as $x^2+px+q=0$

The roots are $1$ and $2$

Sum of roots $=3=-p$

Product of roots $=2=q$

The second equation is $2x^2+3x+1=0$

$2x^2+2x+x+1=0$

$⟹2x(x+1)+1(x+2)=0$

$⟹(x+1)(2x+1)=0$

$⟹x=-1$ or $-1/2$