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(D) Let the correct quadratic equation be $ax^2 + bx + c = 0$ with roots $\alpha$ and $\beta$.The first student copied the constant term incorrectly,b

Vedclass · Accepted Answer

$6, -1$

Vedclass · Answer

(D) Let the correct quadratic equation be $ax^2 + bx + c = 0$ with roots $\alpha$ and $\beta$.The first student copied the constant term incorrectly,but the coefficient of $x^2$ $(a=1)$ and the coefficient of $x$ $(b)$ were correct. The sum of roots is $-b/a$. Since the roots were $3$ and $2$,the sum is $3 + 2 = 5$. Thus,$-b/1 = 5$,which means $b = -5$.The second student copied the constant term $(c = -6)$ and the coefficient of $x^2$ $(a = 1)$ correctly. The product of roots is $c/a = -6/1 = -6$.So,we have the equation $x^2 - 5x - 6 = 0$.Factoring the equation: $x^2 - 6x + x - 6 = 0$.$x(x - 6) + 1(x - 6) = 0$.$(x - 6)(x + 1) = 0$.Therefore,the correct roots are $x = 6$ and $x = -1$.

Two students,while solving a quadratic equation in $x$,one 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:

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