Question

One of the two students while solving a quadratic equation in $x$ copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of $x^2$ correctly 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 $6,-1$

$Letthecorrectequationbe{x}^2+ax-6,$

$Lettheincorrectequationbe{x}^2+ax+b,$

$b=productofroots=2\times 3=6,$

$a=-sumofroots=-(2+3)=-5,$

$Thereforethecorrectequationisgivenby$

$x^2-5x-6=0x^2-6x+x-6=0(x-6)(x+1)=0,x=-1,6$