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Quadrilaterals

If x 2 -11x...

Question

If $x^{2} - 11 x + a$ and $x^{2} - 14 x + 2 a$ have a common factor, then what are the values of $a$ ?

A

0, 7

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B

5, 20

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C

0, 24

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D

1, 3

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Solution

The correct option is C $0, 24$
Let $(x - α)$ be the common factor then
$α^{2} - 11 α + a = 0 & α^{2} - 14 α + 2 a = 0$
Subtract 2 eq $^{n}$ we get $a = 3 α$
$\Rightarrow α^{2} - 11 α + 3 α = 0 \Rightarrow α (α - 8) = 0$
$\Rightarrow α = 0, 8 \Rightarrow a = 0, 24$

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