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Standard IX

Mathematics

Polynomials

Question 2 Wr...

Question

Question 2
Write the coefficients of $x^{2}$ in each of the following:
(i) $2 + x^{2} + x$
(ii) $2 - x^{2} + x^{3}$
(iii) $\frac{π}{2} x^{2} + x$
(iv) $\sqrt{2 x} - 1$

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Solution

(i) In $2 + x^{2} + x,$ coefficient of $x^{2}$ is 1.

(ii) In $2 + x^{2} + x,$ coefficient of $x^{2}$ is - 1.

(iii) $\frac{π}{2} x^{2} + x$ , coefficient of $x^{2}$ is $\frac{π}{2}$ .

(iv) $\sqrt{2 x} - 1, x^{2}$ is not present. Hence, coefficient of $x^{2}$ is 0

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Similar questions

Q. Write the coefficients of

x^{2}

in each of the following:
(i)

2 + x^{2} + x

(ii)

2 - x^{2} + x^{3}

(iii)

\frac{π}{2} x^{2} + x

(iv)

\sqrt{2} x - 1

Q. Find the limits :

i .

lim x \to 1 [\frac{x^{2} + 1}{x + 100}]

i i .

lim x \to 2 [\frac{x^{3} - 4 x^{2} + 4 x}{x^{2} - 4}]

i i i .

lim x \to 2 [\frac{x^{2} - 4}{x^{3} - 4 x^{2} + 4 x}]

i v .

lim x \to 2 [\frac{x^{3} - 2 x^{2}}{x^{2} - 5 x + 6}]

v .

lim x \to 1 [\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}]

Q. Question 2
Write the coefficients of

x^{2}

in each of the following:
(i)

2 + x^{2} + x

(ii)

2 - x^{2} + x^{3}

(iii)

\frac{π}{2} x^{2} + x

(iv)

\sqrt{2 x} - 1

Q. Determine which of the following polynomials has

(x + 1)

a factor:
(i)

x^{3} + x^{2} + x + 1

(ii)

x^{4} + x^{3} + x^{2} + x + 1

(iii)

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

(iv)

x^{3} - x^{2} - (2 + \sqrt{2}) x + \sqrt{2}

Write the coefficient of $x^{2}$ in each of the following?
(1) $2 + x^{2} + x$
(2) $2 - x^{2} + x^{3}$
(3) $\frac{π}{2} x^{2} + x$
(4) $\sqrt{2} x - 1$

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Polynomials

Standard IX Mathematics

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Question 2 Write the coefficients of x2 in each of the following: (i) 2+x2+x (ii) 2−x2+x3 (iii) π2x2+x (iv) √2x−1

(i) In 2+x2+x, coefficient of x2 is 1. (ii) In 2+x2+x, coefficient of x2 is - 1. (iii) π2x2+x, coefficient of x2 is π2. (iv) √2x−1,x2 is not present. Hence, coefficient of x2 is 0

Question 2
Write the coefficients of $x^{2}$ in each of the following:
(i) $2 + x^{2} + x$
(ii) $2 - x^{2} + x^{3}$
(iii) $\frac{π}{2} x^{2} + x$
(iv) $\sqrt{2 x} - 1$

(i) In $2 + x^{2} + x,$ coefficient of $x^{2}$ is 1.

(ii) In $2 + x^{2} + x,$ coefficient of $x^{2}$ is - 1.

(iii) $\frac{π}{2} x^{2} + x$ , coefficient of $x^{2}$ is $\frac{π}{2}$ .

(iv) $\sqrt{2 x} - 1, x^{2}$ is not present. Hence, coefficient of $x^{2}$ is 0