**Samacheer Kalvi 10th Maths Book Back Solution:**

Tamil Nadu **10th Maths Book Back Answers Unit 3 – Algebra Ex 3.9** are provided on this page. Samacheer Kalvi Maths Book Back Solutions/ Guide available for all Units. TN Samacheer Kalvi 10th Maths Book consists of 8 Units and each unit book back solutions given below topics wise with Questions and Answers. The complete** Samacheer Kalvi Books Back Answers/Solutions** are available on our site.

The Samacheer kalvi 10th Maths solutions are useful to enhance your skills. Candidates who prepared for the Competitive and board exams 10th Maths Book Back Answers in English and Tamil Medium. The 10th Maths Unit 3 Algebra consists of 19 units. Each Unit Book Back Answers provide topic-wise on this page. 10th Maths Book Back Answers are prepared according to the latest syllabus. The 10th Maths Book Back Algebra Ex 3.9 Answers in English.

**10th Maths Book Back Answers/Solutions:**

TN Samacheer Kalvi 10th Maths Unit 3 Chapter 9 Book Back Exercise has given below. The 10th Maths Book Back Solutions Guide is uploaded below,

**Chapter 3**

**Exercise 3.9 Algebra**

1.Determine the quadratic equations, whose sum and product of roots are

(i) -9, 20

(ii) 53, 4

(iii) −32, -1

(iv) -(2 – a)^{2}, (a + 5)^{2}

**Solution:**

If the roots are given, general form of the quadratic equation is x^{2} – (sum of the roots) x + product of the roots = 0.

(i) Sum of the roots = -9

Product of the roots = 20

The equation = x^{2} – (-9x) + 20 = 0

⇒ x^{2} + 9x + 20 = 0

(ii) Sum of the roots = 53

Product of the roots = 4

Required equation = x^{2} – (sum of the roots)x + product of the roots

= 0

⇒ x^{2} – 53x + 4 = 0

⇒ 3x^{2} – 5x + 12 = 0

(iii) Sum of the roots = (−32)

(α + β) = −32

Product of the roots (αβ) = (-1)

Required equation = x^{2} – (α + β)x + αβ = 0

x^{2} – (−32)x – 1 = 0

2x^{2} + 3x – 2 = 0

(iv) α + β = – (2 – a)^{2}

αβ = (a + 5)^{2}

Required equation = x^{2} – (α + β)x – αβ = 0

⇒ x^{2} – (-(2 – a)^{2})x + (a + 5)^{2} = 0

⇒ x^{2} + (2 – a)^{2}x + (a + 5)^{2} = 0

2.Find the sum and product of the roots for each of the following quadratic equations

(i) x^{2} + 3x – 28 = 0

(ii) x^{2} + 3x = 0

(iii) 3 + 1a=10a2

(iv) 3y^{2} – y – 4 = 0

(i) x^{2} + 3x – 28 = 0

**Answer:
**Sum of the roots (α + β) = -3

Product of the roots (α β) = -28

(ii) x^{2} + 3x = 0

**Answer:**

Sum of the roots (α + β) = -3

Product of the roots (α β) = 0

(iii) 3 + 1a=10a2

3a^{2} + a = 10

3a^{2} + a – 10 = 0 comparing this with x^{2} – (α + β)

x + αβ = 0

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