Question

Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writting down the constant term and ended up in roots $(4,3)$. Rahul made a mistake in writting down coefficient of $x$ to get roots $(3,2)$. The correct roots of equation are

• A. $-4,-3$
• B. $6,$ $1$
• C. $4,$ $3$
• D. $-6,-1$

Answer 1

Answer: (B)

$6,$ $1$

If $\alpha$ and $\beta$ are roots of a quadratic equation, the equation is $(x-\alpha )(x-\beta )=0$

So according to Sachin, the equation is $(x-4)(x-3)=0\Rightarrow x^2-7x+12=0$

And according to Rahul, the equation is $(x-3)(x-2)=0\Rightarrow x^2-5x+6=0$

Since Sachin made a mistake in writing the constant term, so the correct constant term must be +6

And Rahul made a mistake in writing the coefficient of x so the correct coefficient of x must be -7

Therefore, the quadratic equation is $x^2-7x+6\Rightarrow (x-1)(x-6)=0$

So its roots are 1 and 6 i.e. Option B is correct.