Question

Two students while solving a quadratic equation in $x$, one copied the constant term incorrectly and got the roots as $3$ and $2$. The other copied coefficient of $x$ incorrectly and got roots as $-6$ and $1$ respectively. The correct root(s) is/are (Assume the leading coefficient of the quadratic equation as $1$)

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

Answer 1

Answer: (A), (B)

The correct options are
A $-1$
B $6$

Let the quadratic equation be
$x^2+ax+b=0$
The equation taken by the first student is,
$(x-3)(x-2)=0\Rightarrow x^2-5x+6=0$
Now, as per given condition the student took the constant term incorrectly.
So, the value of $a$ is $-5.$

Now, the equation taken by the second student is
$(x-1)(x+6)=0\Rightarrow x^2+5x-6=0$
Now, as per the given condition the student took the coefficient of $x$ incorrectly.
So, the value of $b$ is $-6.$
Therefore, the quadratic equation is,
$x^2-5x-6=0$
$\Rightarrow x^2-6x+x-6=0\Rightarrow (x-6)(x+1)=0\Rightarrow x=-1,6$