Question

consider the expression x (m2−1) + 3x m 2 , where m is a constant. For what value of m, will the expression be a cubic polynomial?

Answer 1

The given expression is $x^{m^{2}-1 } +3x^{m/2}$, where $m$ is constant.

We have to find what value of $m$, will the expression be cubic polynomial.

Cubic polynomial: A cubic polynomial  is a polynomial of degree $3$.

Here, we can use trail and hit method to solve the given expression.

Now, substitute $m=1$ in the given expression,

$x^{m^{2}-1 } +3x^{m/2}=x^{1^{2}-1 } +3x^{1/2}$

                        $=x^{0} +3x^{1/2}$

                        $=1+3x^{1/2}$

Substitute $m=2$

$x^{m^{2}-1 } +3x^{m/2}=x^{2^{2}-1 } +3x^{2/2}$

                        $=x^{3} +3x$

$x^{3}+3x$ is a cubic polynomial.

Therefore, the value of $m$ is $2$, the given expression will be a cubic polynomial.

Answer 2

Answer:

we know that

a cubic polynomial is a polynomial which has 3 number of zeroes.

so we can use this by hit and trial method

now

let m be 2

x(2square-1)+3x2/2

x(4-1)+3x1/1

x3+3x