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

Options

A. `-4,-3`
B. `6,1`
C. `4,3`
D. `-6,-1`

Answer

B

Explanation

Let the quadratic equation be
`ax^(2)+bx+c=0`
Sachin made a mistake in writing down constant term.
`:.` Sum of the roots is correct.
i.e. `alpha +beta=7`
Rahul made a mistake in writing down coefficient of `x`.
`:.` Product of the roots is correct.
i.e. `alpha beta=6`
`implies` Correct quadratic equation is
`x^(2)-(alpha+beta)x+alpha beta=0`
`impliesx^(2)-7x+6=0`
`implies(x-6)(x-1)=0impliesx=6,1`
Hence correct roots are 1 and 6.