Question

Write the coefficient of $x^{2}$ in each of the following:
i. $2+x^{2}+x$
ii. $2-x^{2}+x^{3}$
iii. $$\dfrac{\pi }{2} x^{2}+x$$
iv. $\sqrt{2} x-1$

Answer 1

Hint: In this question it is given that we have to find the coefficient of $x^{2}$ among the given polynomials. So for this we have to know that if any algebraic expression is given like this, $ax^{3}+bx^{2}+cx+d$ then the coefficient of $x^{2}$ will be the numerical or constant quantity placed before and multiplied with $x^{2}$.

Complete step-by-step answer:

i. $2+x^{2}+x$,
So the above equation can be written as, $x^{2}+x+2$ = $1\times x^{2}+x+2$
Here, 1 is multiplied with $x^{2}$,
Hence the coefficient of $x^{2}$ is 1.

ii. Given $2-x^{2}+x^{3}$
Which can be written as,
$x^{3}-x^{2}+2$
=$x^{3}+(-x^{2})+2$
=$x^{3}+(-1)\cdot x^{2}+2$
So the coefficient of $x^{2}$ is -1.

iii. $$\dfrac{\pi }{2} x^{2}+x$$
So here we can see that $$\dfrac{\pi }{2}$$ is multiplied with $x^{2}$, so therefore, we can say that the coefficient of $x^{2}$ is $$\dfrac{\pi }{2}$$.

iv. $\sqrt{2} x-1$
Now in this expression, there is no $x^{2}$ term, so the coefficient is 0.

Note: To solve this type of question you need to know that if the term that you are asked to find, is negative then you have to make it positive by taking minus in the bracket and the coefficient becomes negative, like we did in the second problem.