RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 10. Quadratic Equations

Subject: Maths - Class 10th

Q. No. 21 of Exercise 10C

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21

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

Given:

taking LCM



cross multiplying


x2 + 1 = 3x


x2 – 3x + 1 = 0


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


a = 1, b = – 3, c = 1


Discriminant D = b2 – 4ac


= (– 3)2 – 4.1.1


= 9 – 4 = 5 >


Hence the roots of equation are real.


√D = √5


Roots α and β 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

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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

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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

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4 x2 + 4bx – (a2 – b2) = 0
33

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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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