Answer
424.2k+ views
Hint: The value of the polynomial can easily be obtained using the given condition. In cases where the condition is given, the best and easiest way to solve is replacing the variables in the polynomial expression with the values mentioned in the condition where the value of the polynomial is to be found out. Here, the given condition is given as $x=0$, hence, we will have to replace the value of x with ‘zero’ in the given polynomial equation as it is the given condition where we have to find the value of the polynomial expression $5x-4{{x}^{2}}+3=0$.
Complete step-by-step solution:
The given polynomial expression is $5x-4{{x}^{2}}+3=0.........................(i)$
We have to find the value of the polynomial expression mentioned in equation (i) at $x=0$. Now, we can find the value of the expression by replacing the value of x in the polynomial equation given above.
Let us firstly assume $P(x)=5x-4{{x}^{2}}+3...................(ii)$
Now, we replace the value of x with ‘zero’ in the above-given equation (ii), then, we get,
$P\left( 0 \right)=5\times 0-4\times {{\left( 0 \right)}^{2}}+3$
$P\left( 0 \right)=0-0+3$
$P\left( 0 \right)=3$
Hence, on replacing the value of x with ‘zero’, we get the value of the given expression as 3, which is the required answer.
Hence, the correct option is option (a).
Note: Students mostly make mistakes will replacing the value and doing the calculation.
An alternate method, to solve this question is to use the remainder theorem. The remainder theorem implies that divide the equation (i) with x. And the remainder left after the entire division process will give the value of the polynomial.
Dividing the polynomial expression $5x-4{{x}^{2}}+3$ with x, we get,
$\Rightarrow x\overline{\left){5x-4{{x}^{2}}+3}\right.}$
$\Rightarrow x\overset{5}{\overline{\left){\begin{align}
& 5x-4{{x}^{2}}+3 \\
& \underline{-5x\text{ }} \\
& 0-4{{x}^{2}} \\
\end{align}}\right.}}$
$\Rightarrow x\overset{5+4x}{\overline{\left){\begin{align}
& 5x-4{{x}^{2}}+3 \\
& \underline{-5x\text{ }} \\
& 0-4{{x}^{2}} \\
& \underline{\text{ +4}{{\text{x}}^{2}}\text{ }}\text{ } \\
& \text{ 0 } \\
\end{align}}\right.}}$
$\Rightarrow x\overset{5+4x}{\overline{\left){\begin{align}
& 5x-4{{x}^{2}}+3 \\
& \underline{-5x\text{ }} \\
& 0-4{{x}^{2}} \\
& \underline{\text{ +4}{{\text{x}}^{2}}\text{ }}\text{ } \\
& \text{ }0+3\text{ } \\
\end{align}}\right.}}$
$\Rightarrow x\overset{5+4x}{\overline{\left){\begin{align}
& 5x-4{{x}^{2}}+3 \\
& \underline{-5x\text{ }} \\
& 0-4{{x}^{2}} \\
& \underline{\text{ +4}{{\text{x}}^{2}}\text{ }}\text{ } \\
& \text{ +}3\text{ } \\
\end{align}}\right.}}$
Since the remainder is 3, so, the value of the expression is 3 at $x=0$.
Complete step-by-step solution:
The given polynomial expression is $5x-4{{x}^{2}}+3=0.........................(i)$
We have to find the value of the polynomial expression mentioned in equation (i) at $x=0$. Now, we can find the value of the expression by replacing the value of x in the polynomial equation given above.
Let us firstly assume $P(x)=5x-4{{x}^{2}}+3...................(ii)$
Now, we replace the value of x with ‘zero’ in the above-given equation (ii), then, we get,
$P\left( 0 \right)=5\times 0-4\times {{\left( 0 \right)}^{2}}+3$
$P\left( 0 \right)=0-0+3$
$P\left( 0 \right)=3$
Hence, on replacing the value of x with ‘zero’, we get the value of the given expression as 3, which is the required answer.
Hence, the correct option is option (a).
Note: Students mostly make mistakes will replacing the value and doing the calculation.
An alternate method, to solve this question is to use the remainder theorem. The remainder theorem implies that divide the equation (i) with x. And the remainder left after the entire division process will give the value of the polynomial.
Dividing the polynomial expression $5x-4{{x}^{2}}+3$ with x, we get,
$\Rightarrow x\overline{\left){5x-4{{x}^{2}}+3}\right.}$
$\Rightarrow x\overset{5}{\overline{\left){\begin{align}
& 5x-4{{x}^{2}}+3 \\
& \underline{-5x\text{ }} \\
& 0-4{{x}^{2}} \\
\end{align}}\right.}}$
$\Rightarrow x\overset{5+4x}{\overline{\left){\begin{align}
& 5x-4{{x}^{2}}+3 \\
& \underline{-5x\text{ }} \\
& 0-4{{x}^{2}} \\
& \underline{\text{ +4}{{\text{x}}^{2}}\text{ }}\text{ } \\
& \text{ 0 } \\
\end{align}}\right.}}$
$\Rightarrow x\overset{5+4x}{\overline{\left){\begin{align}
& 5x-4{{x}^{2}}+3 \\
& \underline{-5x\text{ }} \\
& 0-4{{x}^{2}} \\
& \underline{\text{ +4}{{\text{x}}^{2}}\text{ }}\text{ } \\
& \text{ }0+3\text{ } \\
\end{align}}\right.}}$
$\Rightarrow x\overset{5+4x}{\overline{\left){\begin{align}
& 5x-4{{x}^{2}}+3 \\
& \underline{-5x\text{ }} \\
& 0-4{{x}^{2}} \\
& \underline{\text{ +4}{{\text{x}}^{2}}\text{ }}\text{ } \\
& \text{ +}3\text{ } \\
\end{align}}\right.}}$
Since the remainder is 3, so, the value of the expression is 3 at $x=0$.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)