You can Download Samacheer Kalvi 10th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.8

10th Maths Exercise 3.8 Samacheer Kalvi Question 1.
Find the square root of the following polynomials by division method
(i) x4 – 12x3 + 42x2 – 36x + 9
(ii) 37x2 – 28x3 + 4x4 + 42x + 9
(iii) 16x4 + 8x2 + 1
(iv) 121x4 – 198x3 – 183x2 + 216x + 144
Solution:
The long division method in finding the square root of a polynomial is useful when the degrees of a polynomial is higher.
10th Maths Exercise 3.8 Samacheer Kalvi Chapter 3 Algebra
Ex 3.8 Class 10 Samacheer Maths Solutions Chapter 3 Algebra
10th Maths Exercise 3.8 Samacheer Kalvi Maths Solutions Chapter 3 Algebra

Ex 3.8 Class 10 Samacheer 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:
Exercise 3.8 Class 10 Samacheer Maths Solutions Chapter 3 Algebra

10th Maths Exercise 3.8 Question 3.
Find the values of a and b if the following polynomials are perfect squares
(i) 4x4 – 12x3 + 37x2 + bx + a
(ii) ax4 + bx3 + 361ax2 + 220x + 100
Solution:
(i)
10th Maths Exercise 3.8 In Tamil Samacheer Kalvi Chapter 3 Algebra
Since it is a perfect square.
Remainder = 0
⇒ b + 42 = 0, a – 49 = 0
b = -42, a = 49

(ii) ax4 + bx3 + 361ax2 + 220x + 100
10th Maths 3.8 Samacheer Kalvi Maths Solutions Chapter 3 Algebra
Since remainder is 0
a = 144
b = 264

Exercise 3.8 Class 10 Samacheer Question 4.
Find the values of m and 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) x4 – 8x3 + mx2 + nx + 16
Solution:
(i)
Exercise 3.8 Class 10 Maths Samacheer Kalvi Chapter 3 Algebra

(ii)
10th Maths Exercise 3.8 3rd Sum Samacheer Kalvi Chapter 3 Algebra
Since remainder is 0,
m = 24, n = -32

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