Are these practice questions for Quadratic Equations based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 10 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Quadratic Equations free?

Yes. Every chapter includes free practice questions for Class 10 students to get you started.

What types of questions are included?

The practice set for Quadratic Equations mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Quadratic Equations for full coverage.

How many practice questions are there for Quadratic Equations?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Quadratic Equations Class 10 Mathematics Practice Questions with Answers

easy

Without solving, examine the nature of the roots of the quadratic equation

3x^2 - 5x + 2 = 0

.

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easy

State the condition on the discriminant for a quadratic equation to have no real roots.

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easy

Recall the standard form of a quadratic equation.

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easy

Identify the values of

a, b,

and

c

for the quadratic equation

3x - 5x^2 + 9 = 0

after writing it in standard form.

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easy

Analyze the equation

(x+1)^3 = x^3 + 5x + 7

to determine if it is a quadratic equation. Justify your answer.

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easy

Name the expression

b^2 - 4ac

associated with the quadratic equation

ax^2 + bx + c = 0

.

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easy

Recall the quadratic formula used to find the roots of the equation

ax^2 + bx + c = 0

.

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easy

Define a quadratic equation and provide one example.

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easy

Solve the equation

2x^2 - x + \frac{1}{8} = 0

by factorisation.

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medium

Explain the significance of the condition

a \neq 0

in the definition of a quadratic equation

ax^2 + bx + c = 0

.

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medium

Solve the quadratic equation

4x^2 - 4ax + (a^2 - b^2) = 0

for

x

.

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medium

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Apply this information to calculate their present ages.

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medium

A motorboat, whose speed is

18 \text{ km/h}

in still water, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Formulate a quadratic equation for the speed of the stream. Let the speed of the stream be

x \text{ km/h}

.

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medium

Explain what is meant by a 'root' of a quadratic equation.

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medium

Is it possible to design a rectangular park with a perimeter of

100

m and an area of

700 \text{ m}^2

? Justify your answer by formulating a quadratic equation and evaluating its discriminant, without solving for the dimensions.

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medium

Describe the three possible types of real roots a quadratic equation can have.

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medium

Apply the concept of quadratic equations to find two consecutive odd positive integers, the sum of whose squares is 290.

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medium

Design a word problem involving the ages of two people that can be modeled by the quadratic equation

x^2 + 5x - 300 = 0

, where

x

represents the current age of the younger person.

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medium

A student states that the equation

x^2 + 9 = 0

has no roots. Critique this statement.

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medium

Analyze the equation

x(2x+3) = x^2+1

to determine if it is a quadratic equation and find its roots if it is.

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medium

For the quadratic equation

3x^2 - 7x + 2 = 0

, list the values of

a, b, c

and calculate its discriminant.

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medium

Describe the maximum number of roots a quadratic equation can have and why.

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medium

Critique the following solution for finding the roots of

x^2 - 5x + 6 = 0

. Student's work: "The equation is

x^2 - 5x + 6 = 0

. I need two numbers that add to -5 and multiply to 6. These are -2 and -3. So the roots are

x = -2

and

x = -3

." Identify the error in the reasoning and provide the correct solution.

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medium

Explain the relationship between the zeroes of a quadratic polynomial and the roots of a quadratic equation.

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medium

Calculate the value(s) of

k

for which the quadratic equation

(k+4)x^2 + (k+1)x + 1 = 0

has equal roots.

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medium

A piece of wire of length 40 cm is bent into the form of a rectangle. Calculate the dimensions of the rectangle if its area is

96 \text{ cm}^2

.

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medium

Create a quadratic equation of the form

ax^2 + bx + c = 0

where the coefficients

a, b, c

are integers, and whose roots are

2 + \sqrt{3}

and

2 - \sqrt{3}

.

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medium

Explain the general procedure to determine if a given algebraic equation is quadratic or not.

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medium

Solve the quadratic equation

x^2 - (1+\sqrt{2})x + \sqrt{2} = 0

by factorisation.

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medium

For the quadratic equation

16x^2 - 8x + 1 = 0

, evaluate which method of solving—factorisation or the quadratic formula—is more efficient. Justify your choice.

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medium

Examine if it is possible to design a rectangular garden whose length is 4 meters more than its width and whose area is

140 \text{ m}^2

. If possible, calculate its dimensions.

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hard

Solve for

x

:

\frac{1}{x+4} - \frac{1}{x-7} = \frac{11}{30}

, given

x \neq -4, 7

.

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hard

A company designs a rectangular billboard. The marketing team proposes that the length should be 3 meters more than its width. The design team mandates that a 1-meter wide border must be painted on all sides within the billboard area. If the area of this inner border is required to be exactly

22 \text{ m}^2

, formulate a quadratic equation to find the dimensions of the billboard. Do not solve the equation.

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hard

Compare the equations

(x-a)(x-b) = m^2

and

(x-c)(x-d) = n^2

. Analyze the condition for the first equation to have real roots for all values of

m

.

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hard

A motorboat whose speed is

18 \text{ km/h}

in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Calculate the speed of the stream.

Try solving it in your notebook first, then check the solution.

hard

Summarize how the discriminant,

D = b^2 - 4ac

, determines the nature of the roots for a quadratic equation

ax^2 + bx + c = 0

.

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hard

Identify if the equation

(x+1)^3 = x^3 + 2x + 1

is a quadratic equation. Explain your reasoning.

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hard

Design a scenario for a business that involves calculating a break-even point (where profit is zero). The scenario should lead to the quadratic equation

P(x) = -5x^2 + 100x - 420 = 0

, where

x

is the number of units sold (in thousands) and

P(x)

is the profit (in thousands of rupees). Propose what the values in the equation could represent in the business context.

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hard

A student claims that for the quadratic equation

(k-1)x^2 + 2kx + 4 = 0

, it is possible to find a value of

k

such that the equation has two distinct real roots, two equal real roots, and no real roots. Justify this claim by finding the range of values for

k

for each case.

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hard

Justify the condition on the coefficients

a, b,

and

c

of the quadratic equation

ax^2 + bx + c = 0

(

a \neq 0

) such that its roots are equal in magnitude but opposite in sign.

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hard

Justify why for a quadratic equation

ax^2+bx+c=0

with rational coefficients, if one root is

p + \sqrt{q}

(where

p, q

are rational and

\sqrt{q}

is irrational), then the other root must be its conjugate,

p - \sqrt{q}

.

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hard

Evaluate the statement: "An equation of the form

(x+a)^3 - (x-a)^3 = 0

is always a quadratic equation for any non-zero real number

a

." Justify your conclusion by simplifying the general form of the equation.

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hard

Demonstrate that the equation

(x^2+1)^2 - x^2 = 0

has no real roots by analyzing its discriminant.

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hard

Propose a quadratic equation whose roots are reciprocals of the roots of

2x^2 - 3x - 5 = 0

, without finding the roots of the original equation.

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hard

Consider the equation

x^2 + 2(k+1)x + (k^2+1) = 0

. Evaluate the nature of its roots based on different real values of the parameter

k

. Determine for which values of

k

the equation has real roots, and for which values it has no real roots.

Try solving it in your notebook first, then check the solution.

Quadratic EquationsClass 10 Mathematics Practice Questions