Question

Find the value of the polynomial, \[4{{x}^{2}}-5x+3\] when x = 0.
(a) 1
(b) 2
(c) 3
(d) 4

Answer 1

Hint: To solve this question we first of all should know what is a polynomial, it is an expression of more than 2 algebraic terms of various powers. Here we have to substitute, x = 0 in the given polynomial \[4{{x}^{2}}-5x+3\] to get the result.

Complete step-by-step answer:
A polynomial k is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable.
We are given the polynomial as \[4{{x}^{2}}-5x+3\]. Here we have ‘x’ is the variable of the given polynomial.
We substitute different values to the value to get the value of the polynomial corresponding to that variable value.
Here we have to find the value of possibility \[4{{x}^{2}}-5x+3\] by substituting x = 0 in it.
Let value of polynomial be t,
Then \[t=4{{x}^{2}}-5x+3\].
Substituting x = 0 in above expression we get,
\[\begin{align}
  & t=4\times 0-5\times 0+3 \\
 & \Rightarrow t=0-0+3 \\
 & \Rightarrow t=3 \\
\end{align}\]
Therefore the value of the polynomial \[4{{x}^{2}}-5x+3\] at x = 0 is 3, which is option (c).
So, the correct answer is “Option C”.

Note: If any polynomial has x as denominator of any of terms of it, then x = 0 would give undetermined form and then they are called rational functions. For example if polynomial is of the type \[p\left( x \right)=2x+\dfrac{3}{x}+1\], is rational function and not really a polynomial as it has negative powers of x and it can give undetermined form at some values of x.