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.
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:
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)
Since it is a perfect square.
Remainder = 0
⇒ b + 42 = 0, a – 49 = 0
b = -42, a = 49
(ii) ax4 + bx3 + 361ax2 + 220x + 100
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)
(ii)
Since remainder is 0,
m = 24, n = -32