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Cubic Polynomial

Question 4Wri...

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Question 4
Write the coefficient of $x^{2}$ in each of the following:

(i) $\frac{π}{6} x + x^{2} - 1$

(ii) $3 x - 5$

(iii) $(x - 1) (3 x - 4)$

(iv) $(2 x - 5) (2 x^{2} - 3 x + 1)$

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Solution

(i) The coefficient of $x^{2}$ in $\frac{π}{6} x + x^{2} - 1$ is 1.

(ii) The coefficient of $x^{2}$ in 3x- 5 is 0.

(iii) Let $p (x) = (x - 1) (3 x - 4) = 3 x^{2} - 4 x - 3 x + 4 = 3 x^{2} - 7 x + 4$

Hence, the coefficient of $x^{2}$ in p(x) is 3.

(iv) $L e t p (x) = (2 x - 5) (2 x^{2} - 3 x + 1) = 2 x (2 x^{2} - 3 x + 1) - 5 (2 x^{2} - 3 x + 1) = 4 x^{3} - 6 x^{2} + 2 x - 10 x^{2} + 15 x - 5 = 4 x^{3} - 16 x^{2} + 17 x - 5$
Hence, the coefficient of $x^{2}$ in p(x) is -16.

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Similar questions

Q. Question 4
Write the coefficient of

x^{2}

in each of the following:

(i)

\frac{π}{6} x + x^{2} - 1

3 x - 5

(x - 1) (3 x - 4)

(2 x - 5) (2 x^{2} - 3 x + 1)

Q. Write the coefficient of

x^{2}

in each of the following:

(i)

\frac{π}{6} x + x^{2} - 1

3 x - 5

Q. Write the coefficient of x² in each of the following:

(i) 17 − 2x + 7x²

(ii) 9 − 12x + x³

(iii)

\frac{π}{6} x^{2} - 3 x + 4

\sqrt{3} x - 7

Simplify each of the following and write as a single polynomial.

(i)

(ii)

(iii)

(iv)

(v)

(v)

Write the coefficient of $x^{2}$ in each of the following.

(i) 17 - 2x + 7 $x^{2}$

(ii) 9 - 12x + $x^{3}$

(iii) $\frac{π}{6} x^{2}$ - 3x + 4

(iv) $\sqrt{3}$ x - 7

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Cubic Polynomial

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