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Geometric Progression

If x -2 is ...

Question

If $x - 2$ is a factor of $x^{2} + 3 a x - 2 a$ , then $a$ is equal to

A

2

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B

- 2

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C

1

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D

- 1

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Solution

The correct option is D $- 1$
Let $P (x) = x^{2} + 3 a x - 2 a$
Given, $(x - 2)$ is a factor of $P (x)$
$x - 2 = 0$
$x = 2$
$∴ P (2) = 0$
$\Rightarrow 2^{2} + 3 a (2) - 2 a = 0$
$\Rightarrow 4 + 4 a = 0$
$\Rightarrow a = - 1$
Option D is correct.

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Similar questions

1

is zero of the polynomial

f (x) = a^{2} x^{2} - 3 a x + 3 x - 1

a

I = \int x s i n^{- 1} {\frac{1}{2} \sqrt{\frac{2 a - x}{a}}} d x = \frac{A}{248} (x^{2} - 2 a^{2}) c o s^{- 1} \frac{x}{2 a} - \frac{1}{8} x \sqrt{4 a^{2} - x^{2}} + C

then A is equal to

I = \int \frac{d x}{1 + \sqrt{x^{2} + 2 x + 2}} = \frac{A}{7} log ∣ ∣ x + 1 + \sqrt{x^{2} + 2 x + 2} ∣ ∣ - \frac{\sqrt{x^{2} + 2 x + 2} - 1}{x + 1} + C

then A is equal to

f (x) = ⎧ ⎨ ⎩ \begin{matrix} \frac{x^{2} - (a + 2) x + 2 a}{x - 2}, x \neq 2 2, x = 2 \end{matrix}

is continuous at

x = 2

a

x

from the equations

a x^{2} - 2 a^{2} x + 1 = 0, a^{2} + x^{2} - 3 a x = 0

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