Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.8

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

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.
Samacheer Kalvi 10th Maths Chapter 3 Algebra Ex 3.8 1
Samacheer Kalvi 10th Maths Chapter 3 Algebra Ex 3.8 2
Samacheer Kalvi 10th Maths Chapter 3 Algebra Ex 3.8 3

Synthetic Division Calculator. The calculator will divide the polynomial by the binomial using synthetic division, with steps shown.

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:
Samacheer Kalvi 10th Maths Chapter 3 Algebra Ex 3.8 4

Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 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)
Samacheer Kalvi 10th Maths Chapter 3 Algebra Ex 3.8 5
Since it is a perfect square.
Remainder = 0
⇒ b + 42 = 0, a – 49 = 0
b = -42, a = 49

(ii) ax4 + bx3 + 361ax2 + 220x + 100
Samacheer Kalvi 10th Maths Chapter 3 Algebra Ex 3.8 6
Since remainder is 0
a = 144
b = 264

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)
Samacheer Kalvi 10th Maths Chapter 3 Algebra Ex 3.8 7

(ii)
Samacheer Kalvi 10th Maths Chapter 3 Algebra Ex 3.8 8
Since remainder is 0,
m = 24, n = -32

Leave a Comment

Your email address will not be published. Required fields are marked *

Scroll to Top