Exercise 3.8 - Chapter 3 Algebra 10th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $3.8$
Question 1.
Find the square root of the following polynomials by division method
(i) $x^{4}-12 x^{3}+42 x^{2}-36 x+9$
(ii) $37 \mathrm{x}^{2}-28 \mathrm{x}^{3}+4 \mathrm{x}^{4}+42 \mathrm{x}+9$
(iii) $16 x^{4}+8 x^{2}+1$
(iv) $121 x^{4}-198 x^{3}-183 x^{2}+216 x+144$
Solution:
The long division method in finding the square root of a polynomial is useful when the degrees of a polynomial is higher.

Question $2 .$
Find the square root of the expression $\frac{x^{2}}{y^{2}}-10 \frac{x}{y}+27-10 \frac{y}{x}+\frac{y^{2}}{x^{2}}$

Solution:

Question $3 .$
Find the values of $a$ and $b$ if the following polynomials are perfect squares
(i) $4 x^{4}-12 x^{3}+37 x^{2}+b x+a$
(ii) $a x^{4}+b x^{3}+361 a x^{2}+220 x+100$
Solution:

Question $4 .$
Find the values of $\mathrm{m}$ and $\mathrm{n}$ if the following expressions are perfect squares
(i) $\frac{1}{x^{4}}-\frac{6}{x^{3}}+\frac{13}{x^{2}}+\frac{m}{x}+n$
(ii) $x^{4}-8 x^{3}+m x^{2}+n x+16$

Solution: