# Check whether m=3 is a root of the quadratic equation:

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

Last updated date: 26th Mar 2023

•

Total views: 306k

•

Views today: 2.83k

Answer

Verified

306k+ views

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 ‘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{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 ‘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{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.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE