RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 10. Quadratic Equations

Subject: Maths - Class 10th

Q. No. 3 of Exercise 10C

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3

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

x2 – 6x + 4 = 0

Given: x2 – 6x + 4 = 0

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


a = 1, b = – 6, c = 4


Discriminant D = b2 – 4ac


= (6)2 – 4.1.4


= 36 – 16 = 20 > 0


Hence the roots of equation are real.


Roots are given by





Hence the roots of equation are


Chapter Exercises

Exercise 10A
Exercise 10B
Exercise 10C
Exercise 10D
Exercise 10E
Exercise 10F

More Exercise Questions

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

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