Question

Find the value of the following expression when x=-1
${{x}^{2}}+2x+1$

Answer 1

Hint: In this case the form of the function and the value at which it is to be evaluated is given. Thus, we have to simply put the given value of x in the expression to find the value of the function at that specific value of x.

Complete step-by-step answer:

In the question the functional form of the expression is given as ${{x}^{2}}+2x+1$. We have to evaluate this expression at the point x=-1. Therefore, we can find the different terms of the expression at the given point and add them according to the expression to find the required answer.

At the point, $x=-1$, the first term in the expression will be given by

${{x}^{2}}={{\left( -1 \right)}^{2}}=-1\times -1=1................(1.1)$

And the second term will be given by

$2x=2\times -1=-2...........(1.2)$

And as the third term does not have any x dependence, it will retain the value of 1.

Therefore, from equations (1.1) and (1.2), we obtain

The value of ${{x}^{2}}+2x+1$ at $x=-1$ is equal to $1+(-2)+1=0$.

Therefore, the answer to the given question should be equal to zero.

Note: We could also have used the identity ${{\left( a+b \right)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}$ with a=x and b=1 to find that ${{\left( x+1 \right)}^{2}}={{x}^{2}}+2x+1$ which the expression given in the question. Thus, at x=-1
${{x}^{2}}+2x+1={{\left( x+1 \right)}^{2}}={{\left( -1+1 \right)}^{2}}={{0}^{2}}=0$ which is the same value as obtained by the method given in the solution.