10th Maths Book Back Question and Answers – Chapter 3 Exercise 3.8:

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Samacheer Kalvi 10th Maths Book Back Answers – Ex 3.8 Algebra

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Chapter 3

Exercise 3.8 Algebra

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.

2. Find the square root of the expression x2y2−10xy+27−10yx+y2x2
Solution:

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

4. Find the values of m and n if the following expressions are perfect squares
(i) 1×4−6×3+13×2+mx+n
(ii) x⁴ – 8x³ + mx² + nx + 16
Solution:
(i)

(ii)

Since the remainder is 0,
m = 24, n = -32

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