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

Tamil Nadu **10th Maths Book Back Answers Unit 3 – Algebra Ex 3.14** 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 3.14 Answers in English.

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

TN Samacheer Kalvi 10th Maths Unit 3 Chapter 14 Book Back Exercise has given below. The 10th Maths Book Back Solutions Guide is uploaded below,

**Chapter 3**

**Exercise 3.14 Algebra**

1. Write each of the following expressions in terms of α + β and αβ.

Solution:

2.The roots of the equation 2x^{2} – 7x + 5 = 0 are α and β. Without solving the root find

**Solution:**

2x^{2} – 7x + 5 = x^{2} – 72x+52 = 0

α + β = 72

αβ = 52

3.The roots of the equation x^{2} + 6x – 4 = 0 are α, β. Find the quadratic equation whose roots are

(i) α^{2} and β^{2}

(ii) 2α and 2β

(iii) α^{2}β and β^{2}α

**Solution:
**If the roots are given, the quadratic equation is x

^{2}– (sum of the roots) x + product the roots = 0.

For the given equation.

x

^{2}+ 6x – 4 = 0

α + β = -6

αβ = -4

(i) α

^{2}+ β

^{2}= (α + β)

^{2}– 2αβ

= (-6)

^{2}– 2(-4) = 36 + 8 = 44

α

^{2}β

^{2}= (αβ)

^{2}= (-4)

^{2}= 16

∴ The required equation is x

^{2}– 44x – 16 = 0.

(iii) α^{2}β + β^{2}α = αβ(α + β)

= -4(-6) = 24

α^{2}β × β^{2}α = α^{3}β^{3} = (αβ)^{3} = (-4)^{3} = -64

∴ The required equation = x^{2} – 24x – 64 – 0.

4.If α, β are the roots of 7x^{2} + ax + 2 = 0 and if β – α = −137 Find the values of a.

**Solution:**

5.If one root of the equation 2y^{2} – ay + 64 = 0 is twice the other then find the values of a.

**Solution:**

Let one of the root α = 2β

α + β = 2β + β = 3β

Given

a^{2} = 576

a = 24, -24

6.If one root of the equation 3x^{2} + kx + 81 = 0 (having real roots) is the square of the other then find k.

**Solution:**

3x^{2} + kx + 81 = 0

Let the roots be α and α^{2}

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