The common root of the equations $x^{2} - 7 x + 10 = 0$ and $x^{2} - 10 x + 16 = 0$ is equal to

- 2

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3

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5

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2

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Solution

The correct option is A $2$
Let $α$ be the common root.
Hence substituting $α$ in both, we get
$α^{2} - 7 α + 10 = 0$ ...(i)
$α^{2} - 10 α + 16 = 0$ ...(ii)
Subtracting (ii) from (i) we get ,
$3 α - 6 = 0$
$α = 2$
Hence, common root is $2$ .

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