If $y = (a - 2) x^{2} + (b - 3) x,$ where $a, b \in R$ is a linear function and $| a - b | = 4$ , then the possible value(s) of $b$ is/are

1

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- 2

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6

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Solution

The correct options are
C $- 2$
D $6$
Given: $y = (a - 2) x^{2} + (b - 3) x$
The given function is linear when
$a - 2 = 0 \Rightarrow a = 2$

Now, $| a - b | = 4$
$\Rightarrow a - b = \pm 4 \Rightarrow 2 - b = \pm 4 \Rightarrow - b = - 2 + 4, - 2 - 4 ∴ b = - 2, 6$

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