In a quadratic equation with leading coefficient $1$, a student reads the coefficient of $x$ wrongly as $19$ instead of $16$ and obtains the roots as $-15$ and $-4$. The correct roots are

Using the incorrect roots of -15 and -4 with the leading coefficient of 1, the student formed the equation (x+15)(x+4) = x^2 + 19x + 60, where 60 is the correct constant term. Since the correct coefficient of x is 16, the actual equation is x^2 + 16x + 60 = 0. Factoring this quadratic equation gives (x+6)(x+10) = 0, which means the correct roots are -6 and -10.

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