$x^{2} + 5$ cannot be split into the product of first degree factors.

True

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False

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Solution

The correct option is A
True

Let the first degree factors as (x-a)(x-b).

Then, we have

$x^{2} + 5 = (x - a) (x - b) = x^{2} - (a + b) x + a b$

The above expression gives a+b=0

ab=5

We need to find "a" and "b". For that we need to find (a-b) first using the formula $(a - b)^{2} = (a + b)^{2} - 4 a b$

$\Rightarrow (a - b)^{2} = 0 - 4 (5) = - 20$

The square of no number is negative. So, there are no numbers satisfying the above pair of equations.

Thus $x^{2} + 5$ cannot be split into the product of first degree factors.

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