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

RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 10. Quadratic Equations

Subject: Maths - Class 10^th

Q. No. 1 of Exercise 10C

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1

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

Given: (x – 1)(2x – 1) = 0

2x² – 3x + 1 = 0

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

a = , b = , c = – 1

Discriminant D = b² – 4ac

= (– 3)² – 4.2.1

= 9 – 8 = 1

1

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