What should be added to $x^{2} - 3 x + 8$ to get $2 x^{2} + x - 6$ ?

x^{2} + 4 x - 14

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x^{2} - 4 x + 14

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3 x^{2} + 2 x + 14

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x^{2} - 2 x + 2

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Solution

The correct option is A $x^{2} + 4 x - 14$
Let the expression that should be added be $y$ .

Hence,
$(x^{2} - 3 x + 8) + y = (2 x^{2} + x - 6)$

On rearranging the terms, we get
$y = (2 x^{2} + x - 6) - (x^{2} - 3 x + 8)$

$2 x^{2} + x - 6 x^{2} - 3 x + 8 (-) (+) (-) x^{2} + 4 x - 14$

$y = x^{2} + 4 x - 14$

So, $x^{2} + 4 x - 14$ should be added to $x^{2} - 3 x + 8$ to get $2 x^{2} + x - 6$ .

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