**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) x^{4} – 12x^{3} + 42x^{2} – 36x + 9

(ii) 37x^{2} – 28x^{3} + 4x^{4} + 42x + 9

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

(iv) 121x^{4} – 198x^{3} – 183x^{2} + 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) 4x^{4} – 12x^{3} + 37x^{2} + bx + a

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

**Solution:
**(i)

Since it is a perfect square.

Remainder = 0

⇒ b + 42 = 0, a – 49 = 0

b = -42, a = 49

(ii) ax^{4} + bx^{3} + 361ax^{2} + 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) x^{4} – 8x^{3} + mx^{2} + nx + 16

**Solution:**

(i)

(ii)

Since the remainder is 0,

m = 24, n = -32

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