This page offers a comprehensive collection of practice questions on quadratic equations, including standard quadratic form, fractional quadratic equations, biquadratic equations, and word problems, specially curated for competitive exams and state board examinations. These questions are highly beneficial for students preparing for Haryana CET, SSC exams, Banking exams, Railway exams, and other government job examinations, where quadratic equations and algebra questions are frequently asked.
The practice material is fully aligned with the latest CBSE syllabus and NCERT mathematics curriculum, and is equally useful for PSEB (Punjab School Education Board), HBSE (Haryana Board), and other state board exams for Class 9 and Class 10 Mathematics. Regular practice of these quadratic equation problems helps students improve problem-solving skills, exam speed, and accuracy, especially in fractional and application-based questions, which are considered high-scoring in both board exams and competitive entrance tests.
This free online math practice resource supports self-study, online coaching, and exam-oriented preparation, making it ideal for students searching for NCERT-based practice questions, CBSE maths revision, state board maths preparation, and competitive exam study material related to quadratic equations.
Q.1
Solve the quadratic equation: \(x^2 - 5x + 6 = 0\).
Q.2
Solve: \(x^2 + 7x + 10 = 0\).
Q.3
Solve: \(x^2 - 9 = 0\).
Q.4
Solve: \(2x^2 - 7x + 3 = 0\).
Q.5
Solve: \(x^2 - 4x - 12 = 0\).
Q.6
Solve: \(4x^2 - 25 = 0\).
Q.7
Solve: \(x^2 + x - 20 = 0\).
Q.8
Solve: \(5x^2 - 20x = 0\).
Q.9
Solve: \(x^2 - 13x + 36 = 0\).
Q.10
Solve: \(2x^2 + 3x - 2 = 0\).
Q.11
Solve: \(3x^2 - 5x - 2 = 0\).
Q.12
Solve: \(x^2 + 4x + 1 = 0\).
Q.13
Solve: \(4x^2 + 4x + 1 = 0\).
Q.14
Solve: \(5x^2 + 6x + 1 = 0\).
Q.15
Solve: \(x(x-7)=18\).
Q.16
Solve: \((x-2)(x+5)=0\).
Q.17
Solve: \(x^2 = 3x + 10\).
Q.18
Solve: \((x+1)^2 = 9\).
Q.19
Solve: \(x^2 - 6x + 5 = 0\).
Q.20
Find the quadratic equation whose roots are \(3\) and \(-4\).
Q.21
Solve: \(x^2 + 10x + 25 = 0\).
Q.22
Solve: \(9x^2 - 12x + 4 = 0\).
Q.23
Solve: \(7x^2 + x - 6 = 0\).
Q.24
Solve: \(2x^2 - 3x + 1 = 0\).
Q.25
Solve: \(x^2 + 1 = 2x\).
Q.26
Solve: \(3x^2 = 12x\).
Q.27
Solve: \(x^2 - 2\sqrt{5}x + 5 = 0\).
Q.28
Solve: \(x^2 + 1 = 0\).
Q.29
Find the nature of roots of \(x^2 - 4x + 4 = 0\).
Q.30
Find the nature of roots of \(x^2 + 2x + 5 = 0\).
Q.31
Find \(k\) such that \(x^2 + kx + 9 = 0\) has equal roots.
Q.32
Find \(k\) such that \(x^2 - kx + 16 = 0\) has no real roots.
Q.33
If the roots of \(x^2 - 5x + 6 = 0\) are \(\alpha,\beta\), find \(\alpha^2+\beta^2\).
Q.34
If \(\alpha,\beta\) are roots of \(2x^2 - 3x + 1 = 0\), find \(\alpha\beta\).
Q.35
Find the quadratic equation whose roots are equal and sum to 8.
Q.36
Find two consecutive integers whose product is 56.
Q.37
The sum of two numbers is 9 and their product is 20. Find the numbers.
Q.38
Find two numbers whose difference is 5 and product is 36.
Q.39
The area of a rectangle is 48 sq units. If length exceeds breadth by 2 units, find dimensions.
Q.40
Find two numbers whose sum is 11 and product is 24.
Q.41
Solve: \(2x(x-1)=15\).
Q.42
Solve: \(\frac{1}{x}+\frac{1}{x-2}=1\).
Q.43
Find \(p\) if one root of \(x^2 - px + 16 = 0\) is 4.
Q.44
Solve: \(x^2 - 7x + 10 = 0\).
Q.45
Solve: \(6x^2 - x - 2 = 0\).
Q.46
Solve: \(x^2 + x - 2 = 0\).
Q.47
Solve: \(8x^2 - 2x - 3 = 0\).
Q.48
Solve: \(x^2 - 11x + 28 = 0\).
Q.49
Solve: \(x^2 - 8x + 12 = 0\).
Q.50
Solve: \(10x^2 - 3x - 1 = 0\).
Q.51
The sum of two numbers is 11 and their product is 30. Find the numbers.
Q.52
The difference of two positive numbers is 4 and their product is 45. Find the numbers.
Q.53
Find two consecutive positive integers whose product is 156.
Q.54
The length of a rectangle is 2 m more than its breadth. If the area of the rectangle is 48 sq m, find its dimensions.
Q.55
The product of two consecutive even positive integers is 288. Find the integers.
Q.56
The sum of the squares of two consecutive natural numbers is 365. Find the numbers.
Q.57
The area of a rectangular garden is 96 sq m. If its length is 4 m more than its breadth, find its dimensions.
Q.58
Two numbers differ by 7 and their product is 450. Find the numbers.
Q.59
The hypotenuse of a right-angled triangle is 5 cm more than one of the other sides. If the third side is 12 cm, find the hypotenuse.
Q.60
The product of two natural numbers is 420 and their difference is 1. Find the numbers.
Q.61
Find the quadratic equation whose roots have sum 5 and product 6.
Q.62
Find the quadratic equation whose roots are the reciprocals of the roots of \(x^2 - 4x + 3 = 0\).
Q.63
If the sum and product of the roots of a quadratic equation are 7 and 10 respectively, form the equation.
Q.64
Find the quadratic equation whose roots differ by 2 and whose product is 15.
Q.65
If one root of the quadratic equation \(x^2 - 7x + k = 0\) is the reciprocal of the other, find \(k\).
Q.66
Find the quadratic equation whose roots are \(\alpha+1\) and \(\beta+1\), where \(\alpha,\beta\) are roots of \(x^2 - 3x + 2 = 0\).
Q.67
If the roots of \(x^2 + px + 9 = 0\) are equal, find the value of \(p\).
Q.68
Find the quadratic equation whose roots are the squares of the roots of \(x^2 - 2x - 1 = 0\).
Q.69
If the sum of the roots of a quadratic equation is zero and their product is –9, form the equation.
Q.70
Find the quadratic equation whose roots are \(\alpha-\beta\) and \(\beta-\alpha\), where \(\alpha,\beta\) are roots of \(x^2 - 4x + 1 = 0\).
Q.71
Solve the equation: \(x^4 - 5x^2 + 4 = 0\).
Q.72
Solve: \(x^4 - 9x^2 = 0\).
Q.73
Solve: \(x^4 + 5x^2 + 6 = 0\).
Q.74
Solve: \(2x^4 - 7x^2 + 3 = 0\).
Q.75
Solve: \(x^4 - 4x^2 - 5 = 0\).
Q.76
Solve: \(x^4 + x^2 - 6 = 0\).
Q.77
Solve: \(3x^4 - 12x^2 + 9 = 0\).
Q.78
Solve: \(x^4 - 16 = 0\).
Q.79
Solve: \(x^4 - 7x^2 + 10 = 0\).
Q.80
Solve: \(4x^4 - 13x^2 + 3 = 0\).
Q.81
Find the value of \(k\) for which the quadratic equation \(x^2 + kx + 16 = 0\) has no real roots.
Q.82
If the roots of \(x^2 - 5x + k = 0\) are positive, find the range of \(k\).
Q.83
If one root of the equation \(x^2 - 8x + k = 0\) is 3, find the other root.
Q.84
Find the quadratic equation whose roots are the sum and difference of the roots of \(x^2 - 6x + 5 = 0\).
Q.85
If the roots of \(x^2 + px + 4 = 0\) are equal in magnitude but opposite in sign, find \(p\).
Q.86
If the roots of \(x^2 - 7x + 10 = 0\) are \(\alpha,\beta\), find the quadratic equation whose roots are \(\alpha+2\) and \(\beta+2\).
Q.87
Find the value of \(k\) if the equation \(kx^2 - 6x + 2 = 0\) has equal roots.
Q.88
If the product of the roots of \(x^2 + ax + 9 = 0\) is equal to the sum of the roots, find \(a\).
Q.89
Find the quadratic equation whose roots are \(2\alpha\) and \(2\beta\), where \(\alpha,\beta\) are roots of \(x^2 - 3x + 2 = 0\).
Q.90
If the roots of \(x^2 + kx + 4 = 0\) are real and unequal, find the range of \(k\).
Q.91
The product of two consecutive positive integers is 90. Find the integers.
Q.92
The sum of two numbers is 13 and their product is 40. Find the numbers.
Q.93
The difference of two positive numbers is 5 and their product is 84. Find the numbers.
Q.94
The length of a rectangle is 3 m more than its breadth. If the area of the rectangle is 70 sq m, find its dimensions.
Q.95
The product of two consecutive even positive integers is 360. Find the integers.
Q.96
A train covers a distance of 180 km at a certain speed. If the speed were 15 km/h more, it would take 2 hours less. Find the speed.
Q.97
The sum of the squares of two consecutive natural numbers is 365. Find the numbers.
Q.98
The area of a rectangular park is 221 sq m. If its length is 4 m more than its breadth, find its dimensions.
Q.99
The product of two numbers is 288 and their difference is 12. Find the numbers.
Q.100
The hypotenuse of a right-angled triangle is 10 cm more than one of the other sides. If the third side is 24 cm, find the hypotenuse.
Q.101
Find the quadratic equation whose roots are 3 more than the roots of \(x^2 - 5x + 6 = 0\).
Q.102
If the sum of the roots of a quadratic equation is 7 and their product is 10, find the equation.
Q.103
Find the quadratic equation whose roots are the reciprocals of the roots of \(2x^2 - 3x + 1 = 0\).
Q.104
If one root of the equation \(x^2 - kx + 9 = 0\) is the reciprocal of the other, find the value of \(k\).
Q.105
Find the quadratic equation whose roots differ by 2 and whose product is 15.
Q.106
If \(\alpha,\beta\) are roots of \(x^2 - 4x + 1 = 0\), find the quadratic equation whose roots are \(\alpha^2\) and \(\beta^2\).
Q.107
Find the value of \(k\) for which the quadratic equation \(x^2 + kx + 9 = 0\) has equal roots.
Q.108
Find the quadratic equation whose roots are consecutive positive integers and whose product is 56.
Q.109
If the sum of the squares of the roots of \(x^2 - px + 4 = 0\) is 20, find \(p\).
Q.110
Find the quadratic equation whose roots are \(2+\sqrt{3}\) and \(2-\sqrt{3}\).
Q.111
Solve the equation: \(\dfrac{1}{x} + \dfrac{1}{x-2} = 1\).
Q.112
Solve: \(\dfrac{2}{x} + \dfrac{3}{x-1} = 5\).
Q.113
Solve: \(\dfrac{1}{x} - \dfrac{1}{x-3} = \dfrac{1}{6}\).
Q.114
Solve: \(\dfrac{3}{x} + \dfrac{2}{x+1} = 1\).
Q.115
Solve: \(\dfrac{5}{x} - \dfrac{4}{x-2} = 1\).
Q.116
Solve: \(\dfrac{x}{x-1} + \dfrac{x}{x+1} = 4\).
Q.117
Solve: \(\dfrac{2x}{x-1} - \dfrac{x}{x+1} = 1\).
Q.118
Solve: \(\dfrac{1}{x+2} + \dfrac{1}{x-2} = \dfrac{1}{2}\).
Q.119
Solve: \(\dfrac{3}{x-2} + \dfrac{1}{x+2} = 1\).
Q.120
Solve: \(\dfrac{2}{x} + \dfrac{1}{x+3} = \dfrac{1}{2}\).
Q.121
Find the nature of the roots of the quadratic equation \(x^2 - 4x + 4 = 0\).
Q.122
Find the nature of the roots of \(x^2 + 5x + 6 = 0\).
Q.123
Find the nature of the roots of \(x^2 + 2x + 5 = 0\).
Q.124
Find the nature of the roots of \(4x^2 - 12x + 9 = 0\).
Q.125
Find the nature of the roots of \(3x^2 - 5x - 2 = 0\).
Q.126
For what value of \(k\) does the equation \(x^2 + kx + 9 = 0\) have equal roots?
Q.127
For what values of \(k\) does the equation \(x^2 + kx + 4 = 0\) have no real roots?
Q.128
Find the nature of the roots of \(2x^2 + 3x + 7 = 0\).
Q.129
For what value of \(k\) does the equation \(kx^2 - 6x + 9 = 0\) have equal roots?
Q.130
Find the nature of the roots of \(5x^2 - 20x + 15 = 0\).
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