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Byju's Answer

Standard XII

Mathematics

Roots of a Quadratic Equation

The coefficie...

Question

The coefficient of $x$ in the equation $x^{2} + p x + q = 0$ , was wrongly written as $17$ in place of $13$ and the roots thus found to be $- 2$ and $- 15$ . The roots of the correct equation is/are

- 10

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- 3

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- 15

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Solution

The correct option is B $- 3$
The wrong equation is
$x^{2} + 17 x + q = 0$
As the roots of the this equation are $- 2, - 15$ , sum and product of the roots is,
$- 2 - 15 = - 17 - 2 \times (- 15) = 30 = q$
So, the corrected equation is
$x^{2} + 13 x + 30 = 0 \Rightarrow (x + 10) (x + 3) = 0 ∴ x = - 10, - 3$

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Roots of a Quadratic Equation

Standard XII Mathematics

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The coefficient of x in the equation x2+px+q=0, was wrongly written as 17 in place of 13 and the roots thus found to be −2 and −15. The roots of the correct equation is/are

The correct option is B −3The wrong equation is x2+17x+q=0 As the roots of the this equation are −2,−15, sum and product of the roots is, −2−15=−17−2×(−15)=30=q So, the corrected equation is x2+13x+30=0⇒(x+10)(x+3)=0∴x=−10,−3

The coefficient of $x$ in the equation $x^{2} + p x + q = 0$ , was wrongly written as $17$ in place of $13$ and the roots thus found to be $- 2$ and $- 15$ . The roots of the correct equation is/are