Question

If f(x) =x³-5x²-4x+20 ,find f(1)

Answer 1

Solution :-

The Value of a Polynomial $\mathtt{p (x)}$ at $\mathtt{x = \alpha}$ is obtained by putting $\mathtt {x = \alpha}$ in $\mathtt{p (x)}$ and it is denoted by $\mathtt{p (\alpha)}$.

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So, we have -

$\begin {aligned} \bold {f(x)} &= \bold {x^3 - 5x^2 - 4x + 20}\\\\ \Rightarrow\ &f(1) = 1^3 - 5 \times 1^2 - 4 \times 1 + 20 = (1 - 5 - 4 + 20) = \bold {12}\\\\ \therefore \bold {f(1)} &= \underline {\boxed {\bf 12}}\ \star \end{aligned}$

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Hence, the Value of f(1) is = 12

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Additional Information :-

Polynomials in One Variable :-

An Expression of the form $\mathtt{a_0+a_1x+a_2x^2+...+a_{n-1}x^{n-1}+a_nx^n}$, where $\mathtt{a_0,a_1,a_2,...,a_{n-1}, a_n}$ are Real Numbers, $\mathtt{a_n \neq 0}$ and n is a Non - Negative Integer, is called a Polynomial in x of Degree n.

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Algebraic Expressions :-

A Combination of Constants and Variables, connected by some or all of the Operations $\mathrm{+,\: -,\: \times,\:and\: \div}$, is known as an Algebraic Expression.

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Constants and Variables :-

$\bullet$ A Symbol having a Fixed Numerical Value is called a Constant.

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E.g. $\mathrm {9, -6, \dfrac{4}{7}, \sqrt 2, \pi}$ are all Constants.

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$\bullet$ A Symbol which may be assigned different Numerical Values is known as a Variable.

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E.g. We know that,

The Circumference of a Circle is given by the formula $\mathrm{C = 2 \pi r}$, where r is the Radius of the Circle.

Here, 2 and π are Constants, while C and r are Variables.