Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.8

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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:

Exercise 3.8 Class 10 Samacheer 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

10th Maths Exercise 3.8 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