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${{m}^{2}}+4m+3=0$.

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Hint: Here, we may put the value of m = 2 in the given quadratic equation and check whether the value of the quadratic equation is 0 or not. If it becomes 0 then, 2 will be a root of the given quadratic equation.

Complete step-by-step answer:

The given quadratic equation is:

${{m}^{2}}+4m+3=0.........(1)$

Since, we know that the meaning of the root of an equation is that at that particular value, the value of the function becomes zero.

Let us consider a quadratic equation $a{{x}^{2}}+bx+c=0$, where a, b and c are real numbers.

Now, if a real number â€˜pâ€™ is a root of this quadratic equation then the value of this equation at p will be zero. Or we can say that:

$a{{p}^{2}}+bp+c=0$ that is when we substitute p in place of x in this equation the value of the equation becomes zero.

So, for the quadratic equation given in the question to check whether m=2 is a root of this equation or not, we may substitute 2 in place of m in equation (1). So, on substituting the value we get:

$\begin{align}

& {{\left( 2 \right)}^{2}}+4\times 2+3 \\

& =4+8+3 \\

& =15 \\

\end{align}$

So, we get 15 on substituting m=2 in the given quadratic equation which is not equal to zero.

Hence, m=2 is not a root of the given quadratic equation ${{m}^{2}}+4m+3=0$.

Note: Students should note here that the geometrical meaning of the root of an equation is that the graph of the function of that equation cuts the x-axis at this point. So, such questions can also be solved by plotting a graph of the given equation and then checking whether it cuts the x-axis at x=2 or not.

Complete step-by-step answer:

The given quadratic equation is:

${{m}^{2}}+4m+3=0.........(1)$

Since, we know that the meaning of the root of an equation is that at that particular value, the value of the function becomes zero.

Let us consider a quadratic equation $a{{x}^{2}}+bx+c=0$, where a, b and c are real numbers.

Now, if a real number â€˜pâ€™ is a root of this quadratic equation then the value of this equation at p will be zero. Or we can say that:

$a{{p}^{2}}+bp+c=0$ that is when we substitute p in place of x in this equation the value of the equation becomes zero.

So, for the quadratic equation given in the question to check whether m=2 is a root of this equation or not, we may substitute 2 in place of m in equation (1). So, on substituting the value we get:

$\begin{align}

& {{\left( 2 \right)}^{2}}+4\times 2+3 \\

& =4+8+3 \\

& =15 \\

\end{align}$

So, we get 15 on substituting m=2 in the given quadratic equation which is not equal to zero.

Hence, m=2 is not a root of the given quadratic equation ${{m}^{2}}+4m+3=0$.

Note: Students should note here that the geometrical meaning of the root of an equation is that the graph of the function of that equation cuts the x-axis at this point. So, such questions can also be solved by plotting a graph of the given equation and then checking whether it cuts the x-axis at x=2 or not.

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