**10th Maths Book Back Question and Answers – Chapter 3 Exercise 3.14:**

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**Samacheer Kalvi 10th Maths Book Back Answers – Ex 3.14 Algebra**

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**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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