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Standard XII

Mathematics

Sufficient Condition for an Extrema

In a quadrati...

Question

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

6, 10

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- 6, - 10

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- 7, - 9

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- 12, - 4

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Solution

The correct option is A $- 6, - 10$
The coefficient of $x$ is wrongly read.
$∴$ Sum of roots $= - \frac{b}{a}$ is wrong as value of $b$ is interpreted wrong.
However, we can evaluate the product of the roots
Product of roots $= \frac{c}{a} = (- 15) \times (- 4) = 60$
As we know that $x^{2} -$ (sum of roots) $x +$ product of roots $= 0$ is the quadratic equation when sum of roots and product of roots are given.
So, the equation becomes $x^{2} + 16 x + 60 = 0$
$x = - 10, - 6$ .

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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

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