The zeroes of a polynomial $p (x) = a x^{2} + b x + 2$ are 1 and 2
Which of the following are statements is/are true?

a + b + 2 = 0

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a + 2 b + 2 = 0

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a + b + 1 = 0

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5 a + 3 b + 4 = 0

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Solution

The correct options are
A $a + b + 2 = 0$
D $5 a + 3 b + 4 = 0$
Given 1 and 2 are zeroes of $p (x)$
$\Rightarrow p (1) = 0 a n d p (2) = 0$
$∴$
$p (1)$ = $a + b + 2 = 0$ ......(i)

Also,
$p (2) = 4 a + 2 b + 2 = 0$ .....(ii)

Adding equations (i) and (ii), we get
$5 a + 3 b + 4 = 0$

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