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Answer:

with solution

Step-by-step explanation:

1. 2x² + 7x + 5 = 0

a = 2 b = 7 c = 5

Discriminant:

b² - 4ac = 7² - 4(2)(5)

= 49 - 40

= 9

Nature of the roots: real, distinct and rational

2. 8x² + 8x - 2 = 0

a = 8 b = 8 c = -2

Discriminant:

b² - 4ac = 8² - 4(8)(-2)

= 64 + 64

= 128

Nature of the roots: real, distinct and irrational

3. 3x² + 8x + 5 = 0

a = 3 b = 8 c = 5

Discriminant:

b² - 4ac = 8² - 4(3)(5)

= 64 - 60

= 4

Nature of the roots: real, distinct and rational

4. 3x² + 7x + 1 = 0

a = 3 b = 7 c = 1

Discriminant:

b² - 4ac = 7² - 4(3)(1)

= 49 - 12

= 37

Nature of the roots: real, distinct and irrational

5. 2x² + 6x + 5 = 0

a = 2 b = 6 c = 5

Discriminant:

b² - 4ac = 6² - 4(2)(5)

= 36 - 40

= -4

Nature of the roots: imaginary

6. 4x² + 12x +9= 0

a = 4 b = 12 c = 9

Discriminant:

b² - 4ac = 12² - 4(4)(9)

= 144 - 144

= 0

Nature of the roots: real, equal and rational

7. 5x² + 3x + 1 = 0

a = 5 b = 3 c = 1

Discriminant:

b² - 4ac = 3² - 4(1)(5)

= 9 - 20

= -11

Nature of the roots: imaginary

8. 3x² + 5x - 2 = 0

a = 3 b = 5 c = -2

Discriminant:

b² - 4ac = 5² - 4(3)(-2)

= 25 + 24

= 49

Nature of the roots: real, distinct and rational

9. 5x² + 10x + 6 = 0

a = 5 b = 10 c = 6

Discriminant:

b² - 4ac = 10² - 4(5)(6)

= 100 - 120

= -20

Nature of the roots: imaginary

10. 3x² - 12x + 12 = 0

a = 3 b = -12 c = 12

Discriminant:

b² - 4ac = -12² - 4(3)(12)

= 144 - 144

= 0

Nature of the roots: real, equal and rational

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