Question

Check whether m=2 is a root of the quadratic equation:
${{m}^{2}}+4m+3=0$.

Answer 1

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.

Complete step-by-step solution
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 ‘p’ 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:
$\begin{aligned} & {{\left( 2 \right)}^{2}}+4\times 2+3 \\\ & =4+8+3 \\\ & =15 \\\ \end{aligned}$
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.