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) x^{4} – 12x^{3} + 42x^{2} – 36x + 9

Answer:

(ii) 31 x^{2} – 28x^{3} + 4x^{4} + 42x + 9

Answer:

Rearrange the order we get

4x^{4} – 28x^{3} + 37x^{2} + 42x + 9

(iii) 16x^{4} + 8x^{2} + 1

Answer:

(iv) 121 x^{4} – 198x^{3} – 183x^{2} + 216x + 144

Answer:

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:

Question 3.

Find the values of a and b if the following polynomials are perfect squares.

(i) 4x^{4} – 12x^{3} + 37x^{2} + bx + a

Answer:

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) ax^{4} + bx^{3} + 361x^{2} + 220x + 100

Answer:

Re-arrange the order we get

100 + 220x + 361x^{2} + bx^{3} + ax^{4}

Since it is a perfect square

b – 264 = 0

b = 264

a – 144 = 0

a = 144

∴ The value of a = 144 and b = 264

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:

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

(ii) x^{4} – 8x^{3} + mx^{2} + nx + 16

Answer:

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