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Nature of Roots

All the integ...

Question

All the integral values of $a$ for which the quadratic equation $(x - a) (x - 10) + 1 = 0$ has integral roots, are

A

11, 12

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B

9, 12

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C

8, 12

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D

8, 11

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Solution

The correct option is C $8, 12$
$(x - a) (x - 10) = - 1;$ where $x, a \in Z$
The product of two integers is $- 1$ .
$∴ x - a = 1$ and $x - 10 = - 1$
or $x - a = - 1$ and $x - 10 = 1$

If $x - 10 = - 1$ , then $x = 9$
$\Rightarrow a = 8$
If $x - 10 = 1$ , then $x = 11$
$\Rightarrow a = 12$

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Nature of Roots

Standard XIII Mathematics

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