Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8

Students can download Maths Chapter 3 Algebra Ex 3.8 Questions and Answers, Notes, Samacheer Kalvi 10th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

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
Answer:
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8 1
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8

(ii) 31 x2 – 28x3 + 4x4 + 42x + 9
Answer:
Rearrange the order we get
4x4 – 28x3 + 37x2 + 42x + 9
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8 3
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8

(iii) 16x4 + 8x2 + 1
Answer:
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8 5
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8 6

(iv) 121 x4 – 198x3 – 183x2 + 216x + 144
Answer:
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8 7
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8 8

Question 2.
Find the square root of the expression
\(\frac{x^{2}}{y^{2}}\) – \(\frac { 10x }{ y } \) + 27 – \(\frac { 10y }{ x } \) + \(\frac{y^{2}}{x^{2}}\)
Answer:
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8 11
Samacheer Kalvi 10th Maths Guide 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
Answer:
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8 112
Since it is a perfect square
b + 42 = 0
b = – 42
a – 49 = 0
a = 49
∴ The value of a = 49 and b = – 42

(ii) ax4 + bx3 + 361x2 + 220x + 100
Answer:
Re-arrange the order we get
100 + 220x + 361x2 + bx3 + ax4
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8 12
Since it is a perfect square
b – 264 = 0
b = 264
a – 144 = 0
a = 144
∴ The value of a = 144 and b = 264

Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8

Question 4.
Find the values of m and n if the following expressions are perfect sqaures.
(i) \(\frac{1}{x^{4}}\) – \(\frac{6}{x^{3}}\) + \(\frac{13}{x^{2}}\) + \(\frac { m }{ x } \) + n
Answer:
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8 13
Since it is a perfect square
\(\frac { 1 }{ x } \) (m + 12) = 0
m + 12 = 0
m = -12
n – 4 = 0
n = 4
∴ The value of m = -12 and n = 4

Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8

(ii) x4 – 8x3 + mx2 + nx + 16
Answer:
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.8 14
Since it is a perfect square
m – 16 – 8 = 0
m – 24 = 0
m = 24
n + 32 = 0
n = -32
∴ The value of m = 24 and n = -32

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