(B) Let the incorrect equation be $x^2 + 17x + q = 0$. Given the roots are $-2$ and $-15$,the product of the roots is $(-2) \times (-15) = 30$. Since

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(B) Let the incorrect equation be $x^2 + 17x + q = 0$. Given the roots are $-2$ and $-15$,the product of the roots is $(-2) \times (-15) = 30$. Since the constant term $q$ was not changed,$q = 30$. The original equation is $x^2 + 13x + 30 = 0$. Factoring the equation: $x^2 + 10x + 3x + 30 = 0$. $x(x + 10) + 3(x + 10) = 0$. $(x + 3)(x + 10) = 0$. Thus,the roots are $x = -3$ and $x = -10$.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Relation between roots and coefficients

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The coefficient of $x$ in the equation $x^2 + px + q = 0$ was taken as $17$ in place of $13$. Its roots were found to be $-2$ and $-15$. The roots of the original equation are:

IIT 1977 All IIT

IIT 1979 All IIT

A
$3, 10$
B
$-3, -10$
C
$-5, -18$
D
None of these

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2 Complex Numbers and Quadratic Equations: Quadratic Equations

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Relation between roots and coefficients

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The coefficient of $x$ in the equation $x^2 + px + q = 0$ was taken as $17$ in place of $13$. Its roots were found to be $-2$ and $-15$. The roots of the original equation are:

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