The polynomial x 2- a cannot be factorized if a -0-A- TrueB- False

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Standard IX

Mathematics

Factorisation of Quadratic Polynomials - Factor Theorem

The polynomia...

Question

The polynomial $(x^{2} + a)$ cannot be factorized if $a > 0$ .

True

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False

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Solution

The correct option is A
True

Suppose α be the zero of the polynomial. then $α^{2} + a$ will be equal to zero

$α^{2} + a = 0$

$α^{2} = - a$

but the square of any number cannot be negative.

So there will be no $α$ such that $α^{2}$ is negative.

$(x^{2} + a)$ cannot be factorized if $a > 0$ . So the given statement is true.

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The polynomial (x2+a) cannot be factorized if a>0.

The correct option is A True Suppose α be the zero of the polynomial. then α2+a will be equal to zero α2+a=0 α2=−a but the square of any number cannot be negative. So there will be no α such that α2 is negative. (x2+a) cannot be factorized if a>0. So the given statement is true.

The polynomial $(x^{2} + a)$ cannot be factorized if $a > 0$ .