If the coefficient of $x$ in the quadratic equation $x^{2}+px+q=0$ was taken as $17$ in place of $13$, then its roots were found to be $-2$ and $-15$. The roots of the original equation are

The incorrectly recorded equation was x^2 + 17x + q = 0, and its roots are given as -2 and -15. We find the constant term q by multiplying the roots: (-2) * (-15) = 30. The original equation is x^2 + 13x + 30 = 0. Factoring this gives (x + 3)(x + 10) = 0, so the roots of the original equation are -3 and -10.

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