1. Tardigrade
  2. Question
  3. Mathematics
  4. Two candidates attempt to solve a quadratic equation x2 + px + q = 0. One start with a wrong value of p and gets 2, 6 as its roots and other start with a wrong value of q and obtained roots 2, - 9. The correct roots are

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Two candidates attempt to solve a quadratic equation $x^2 + px + q = 0$. One start with a wrong value of $p$ and gets $2, 6$ as its roots and other start with a wrong value of $q$ and obtained roots $2, - 9$. The correct roots are

Complex Numbers and Quadratic Equations

Solution:

Consider $x^{2}+p x+q=0$, by assuming $\alpha, \beta$ as correct roots $\therefore \quad \alpha \beta=q=2 \times 6=12$
the wrong value of $p$ effects only the sum of the roots and not the product, we need $p$. Now, again for second candidate, assume value of $p$ is correct. $\therefore \quad \alpha+\beta=p=2+(-9)=-7$
$\therefore $ the correct equation is
$x^{2}-($ Sum of roots $) x+$ product of roots $=0$ or
$x^{2}+7 x+12= 0$
$ \Rightarrow x=-3,-4$