Check whether m=3 is a root of the quadratic equation:
${{m}^{2}}+4m+3=0$.
Answer
361.5k+ 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.
Last updated date: 30th Sep 2023
•
Total views: 361.5k
•
Views today: 3.61k
Recently Updated Pages
What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

One cusec is equal to how many liters class 8 maths CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE
