Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 10. Quadratic Equations

Subject: Maths - Class 10^th

Q. No. 22 of Exercise 10C

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22

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

Given:

taking LCM

3x² – 6x + 2 = 0 cross multiplying

Comparing with standard quadratic equation ax² + bx + c = 0

a = 3, b = – 6, c = 2

Discriminant D = b² – 4ac

= (– 6)² – 4.3.2

= 36 – 24 = 12 > 0

Hence the roots of equation are real.

Roots are given by

Hence the roots of equation are

22

Chapter Exercises

Exercise 10A

Exercise 10B

Exercise 10C

Exercise 10D

Exercise 10E

Exercise 10F

1

Find the discriminant of each of the following equations:
2x² – 7x + 6 = 0

1

Find the discriminant of each of the following equations:
3x² – 2x + 8 = 0

1

Find the discriminant of each of the following equations:
2x² – 5√x + 4 = 0

1

Find the discriminant of each of the following equations:
√3x² + 2√2x – 2√3 = 0

1

Find the discriminant of each of the following equations:
(x – 1)(2x – 1) = 0

1

Find the discriminant of each of the following equations:
1 – x = 2x²

2

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x² – 4x – 1 = 0

3

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x² – 6x + 4 = 0

4

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
2x² + x – 4 = 0

5

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
25x² + 30x + 7 = 0

6

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
16x² = 24x + 1

7

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
15x² – 28 = x

8

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
2x² – 2√2x + 1 = 0

9

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
√2x² + 7x + 5√2 = 0

10

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
√3x² + 10x – 8√3 = 0

11

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
√3x² – 2√2x –2√3 = 0

12

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
2x² + 6√3x – 60 = 0

13

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
4√3x² + 5x – 2√3 = 0

14

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
3x² –2√6x + 2 = 0

15

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
2√3x² – 5x + √3 = 0

16

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x² + x + 2 = 0

17

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
2x² + ax – a² = 0

18

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x² – (√3 + 1) x + √3 = 0

19

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
2x² + 5√3x + 6 = 0

20

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
3x² – 2x + 2 = 0

21

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

22

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

23

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

24

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

25

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
36x² – 12ax + (a² – b²) = 0

26

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x² – 2ax + (a² – b²) = 0

27

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x² – 2ax – (4b² – a²) = 0

28

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x² + 6x – (a² + b² – 8) = 0

29

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x² + 5x – (a² + a – 6) = 0

30

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x² – 4ax – b² + 4a² = 0

31

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
4 x² – 4a²x + (a⁴ – b⁴) = 0

32

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
4 x² + 4bx – (a² – b²) = 0

33

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x² – (2b – 1)x + (b² – b – 20) = 0

34

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
3a²x² + 8abx + 4b² = 0, a ≠ 0

35

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
a²b²x² – (4b⁴ – 3a⁴)x – 12a²b² = 0, a ≠ 0 and b ≠ 0

36

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
12abx² – (9a² – 8b²)x – 6ab = 0, where a ≠ 0 and b ≠ 0