Question

Two students are solving a quadratic equation in $x$. One copied the constant term incorrectly and got the roots as $3$ and $2$. The other copied the correct constant term and co-efficient of $x^2$ as $-6$ and $1$ respectively. The correct roots are

• A. $3,-2$
• B. $-3,2$
• C. $-6,-1$
• D. $6,-1$

Answer 1

The correct option is D $6,-1$

The roots obtained after considering the incorrect constant term won't affect the sum of roots as we know sum of roots $=-\frac{b}{a}$.
It is irrespective of the constant term so the sum of roots can be calculated by the roots obtained by equation with wrong coefficient $=2+3=5$
Now, we can get the equation $a{x}^2+bx+c=0$ as it is given that $-\frac{b}{a}=5,a=1,c=-6$
So, the equation becomes $x^2-5x-6$
$(x-6)(x+1)$
$x=-1,6$
Hence, option D.