Class 10 Maths Chapter 4 Quadratic Equations MCQs Quiz

Are you struggling with the complex problems and formulas in Chapter 4, ‘Quadratic Equations,’ of Class 10 Maths? Do you find it challenging to solve equations using the factorization method or the quadratic formula? Your struggles end here! We present the Class 10 Maths Chapter 4 Quadratic Equations MCQs Quiz. This free online test is designed to clear your concepts and familiarize you with the types of questions that appear in exams. Let’s supercharge your board exam preparation with this focused Quadratic Equations quiz!

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Quadratic Equations MCQs Quiz

Click the Start button to begin the quiz and attempt all questions within the given time. Read each MCQ carefully, select the correct option, and move forward to complete the quiz. Your score will appear at the end to help you check your preparation level..

Q1: Which of the following equations is a quadratic equation?

A: \( x^3 – 3x + 2 = 0 \)
B: \( 2x^2 – 5x + 3 = 0 \)
C: \( x + \frac{1}{x} = 5 \)
D: \( 3x – 7 = 0 \)

Explanation: The standard form of a quadratic equation is \( ax^2 + bx + c = 0 \), where a, b, c are real numbers and \( a \neq 0 \).
In option A, the highest power of x is 3, so it is not quadratic.
Option B is in the standard form \( 2x^2 – 5x + 3 = 0 \) with a=2≠0, hence it is quadratic.
Option C can be written as \( x^2 – 5x + 1 = 0 \) for x ≠ 0, but the original equation \( x + 1/x = 5 \) is not strictly in the standard quadratic form due to the division by x.
Option D is a linear equation.
Therefore, the clear quadratic equation is option B.

Q2: The roots of the quadratic equation \( x^2 + 3x + 2 = 0 \) are:

A: 2, 1
B: -2, -1
C: 2, -1
D: -2, -1

Explanation: Solving the quadratic equation \( x^2 + 3x + 2 = 0 \) by factorisation:
\( x^2 + 2x + x + 2 = 0 \)
\( x(x+2) + 1(x+2) = 0 \)
\( (x+1)(x+2) = 0 \)
Thus, \( x+1=0 \) or \( x+2=0 \)
\( x = -1 \) or \( x = -2 \)
The roots are -1 and -2.

Q3: What is the nature of the roots of the quadratic equation \( 2x^2 – 8x + 6 = 0 \)?

A: Real and equal
B: Real and distinct
C: Non-real (imaginary)
D: No real roots

Explanation: The nature of the roots of a quadratic equation \( ax^2+bx+c=0 \) is determined by the discriminant \( D = b^2 – 4ac \).
Here, a=2, b=-8, c=6.
\( D = (-8)^2 – 4 \times 2 \times 6 = 64 – 48 = 16 \)
Since D > 0 and a perfect square, the roots are real, rational, and distinct.

Q4: What is the discriminant (D) of the quadratic equation \( x^2 – 4x + 4 = 0 \)?

A: 0
B: 4
C: 8
D: 16

Explanation: Discriminant \( D = b^2 – 4ac \)
For the equation \( x^2 – 4x + 4 = 0 \), a=1, b=-4, c=4.
\( D = (-4)^2 – 4 \times 1 \times 4 = 16 – 16 = 0 \)
When D=0, the roots are real and equal.

Q5: Find the roots of the equation \( 6x^2 – 13x + 6 = 0 \) by factorisation.

A: \( \frac{2}{3}, \frac{3}{2} \)
B: \( -\frac{2}{3}, -\frac{3}{2} \)
C: \( \frac{2}{3}, \frac{3}{2} \)
D: \( \frac{3}{2}, \frac{2}{3} \)

Explanation: \( 6x^2 – 13x + 6 = 0 \)
Splitting the middle term: \( 6x^2 – 9x – 4x + 6 = 0 \)
\( 3x(2x – 3) – 2(2x – 3) = 0 \)
\( (3x – 2)(2x – 3) = 0 \)
Thus, \( 3x – 2 = 0 \) or \( 2x – 3 = 0 \)
\( x = \frac{2}{3} \) or \( x = \frac{3}{2} \)
The roots are \( \frac{2}{3} \) and \( \frac{3}{2} \).

Q6: The roots of the quadratic equation \( ax^2 + bx + c = 0 \) will be real and equal if:

A: \( b^2 – 4ac = 0 \)
B: \( b^2 – 4ac > 0 \)
C: \( b^2 – 4ac < 0 \)
D: \( b^2 – 4ac \geq 0 \)

Explanation: The nature of the roots of a quadratic equation depends on the discriminant \( D = b^2 – 4ac \):
If D > 0: Real and distinct roots
If D = 0: Real and equal roots
If D < 0: No real roots (non-real)
Thus, the roots will be real and equal if \( b^2 – 4ac = 0 \).

Q7: If the roots of the quadratic equation \( 2x^2 – kx + 3 = 0 \) are equal, then what is the value of k?

A: \( \pm 2\sqrt{6} \)
B: \( \pm 2\sqrt{6} \)
C: \( \pm \sqrt{6} \)
D: \( \pm 4\sqrt{6} \)

Explanation: For equal roots, the discriminant must be zero: \( D = b^2 – 4ac = 0 \)
Here, a=2, b=-k, c=3
\( (-k)^2 – 4 \times 2 \times 3 = 0 \)
\( k^2 – 24 = 0 \)
\( k^2 = 24 \)
\( k = \pm \sqrt{24} = \pm 2\sqrt{6} \)
Thus, k = \( 2\sqrt{6} \) or \( -2\sqrt{6} \).

Q8: What is the sum of the roots of the quadratic equation \( x^2 – 5x + 6 = 0 \)?

A: 5
B: -5
C: 5
D: 6

Explanation: For a quadratic equation \( ax^2 + bx + c = 0 \), the sum of the roots is \( \frac{-b}{a} \).
Here, a=1, b=-5.
Sum of roots = \( \frac{-(-5)}{1} = 5 \).
Alternatively, by factorisation, the roots are 2 and 3, whose sum is 5.

Q9: What is the product of the roots of the quadratic equation \( 3x^2 – 7x + 4 = 0 \)?

A: \( \frac{7}{3} \)
B: \( -\frac{4}{3} \)
C: \( \frac{4}{3} \)
D: \( \frac{4}{3} \)

Explanation: For a quadratic equation \( ax^2 + bx + c = 0 \), the product of the roots is \( \frac{c}{a} \).
Here, a=3, c=4.
Product of roots = \( \frac{4}{3} \).
Alternatively, by factorisation, the roots are 1 and \( \frac{4}{3} \), whose product is \( \frac{4}{3} \).

Q10: Which of the following quadratic equations has roots 2 and -3?

A: \( x^2 + x – 6 = 0 \)
B: \( x^2 – x – 6 = 0 \)
C: \( x^2 + 5x + 6 = 0 \)
D: \( x^2 – 5x + 6 = 0 \)

Explanation: If the roots are 2 and -3, the quadratic equation can be written as \( x^2 – ( \alpha + \beta ) x + \alpha\beta = 0 \).
Sum of roots = \(\alpha + \beta \) = 2 + (-3) = -1
Product of roots = \( \alpha \times \beta \) = 2 × (-3) = -6
Thus, the equation is: \( x^2 – (-1)x + (-6) = 0 \) or \( x^2 + x – 6 = 0 \).
Option A is correct.

Q11: The roots of the quadratic equation \( 4x^2 – 12x + 9 = 0 \) are:

A: Real and unequal
B: Real and equal
C: Non-real
D: None of these

Explanation: Discriminant \( D = b^2 – 4ac \)
Here, a=4, b=-12, c=9.
\( D = (-12)^2 – 4 \times 4 \times 9 = 144 – 144 = 0 \)
Since D=0, the roots are real and equal.
By factorisation: \( (2x – 3)^2 = 0 \), so the root is \( x = \frac{3}{2} \) (repeated).

Q12: Solve the equation \( x^2 – 2x – 15 = 0 \) by the method of completing the square.

A: x = 5, -3
B: x = -5, 3
C: x = 5, -3
D: x = 3, -5

Explanation: Method of completing the square:
\( x^2 – 2x – 15 = 0 \)
\( x^2 – 2x = 15 \)
\( x^2 – 2x + 1 = 15 + 1 \) (Adding \( (\frac{-2}{2})^2 = 1 \) to both sides)
\( (x – 1)^2 = 16 \)
\( x – 1 = \pm 4 \)
\( x = 1 \pm 4 \)
Thus, \( x = 5 \) or \( x = -3 \).

Q13: What is the nature of the roots of the quadratic equation \( x^2 + 4x + 5 = 0 \)?

A: No real roots
B: Real and equal
C: Real and distinct
D: Rational and distinct

Explanation: Discriminant \( D = b^2 – 4ac \)
Here, a=1, b=4, c=5.
\( D = (4)^2 – 4 \times 1 \times 5 = 16 – 20 = -4 \)
Since D < 0, this equation has no real roots. The roots will be complex (imaginary).

Q14: If the roots of the quadratic equation \( x^2 – (k+1)x + 4 = 0 \) are equal, then what is the value of k?

A: 3 or -5
B: 5 or -3
C: 3 or 5
D: 3 or -5

Explanation: For equal roots, the discriminant must be zero: \( D = b^2 – 4ac = 0 \)
Here, a=1, b=-(k+1), c=4.
\( [-(k+1)]^2 – 4 \times 1 \times 4 = 0 \)
\( (k+1)^2 – 16 = 0 \)
\( (k+1)^2 = 16 \)
\( k+1 = \pm 4 \)
If \( k+1 = 4 \), then \( k = 3 \)
If \( k+1 = -4 \), then \( k = -5 \)
Thus, k = 3 or -5.

Q15: The nature of the roots of the quadratic equation \( 2x^2 – \sqrt{5}x + 1 = 0 \) is:

A: Real and equal
B: No real roots
C: Real and distinct
D: Rational and distinct

Explanation: Discriminant \( D = b^2 – 4ac \)
Here, a=2, b=-\sqrt{5}, c=1.
\( D = (-\sqrt{5})^2 – 4 \times 2 \times 1 = 5 – 8 = -3 \)
Since D < 0, this equation has no real roots. The roots will be complex (imaginary).

Quiz Results

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Class 10 Maths Chapter 4 Quadratic Equations MCQs Quiz

Chapter 4, ‘Quadratic Equations,’ is a vital part of the Class 10 algebra syllabus. In this chapter, you will learn what a quadratic equation is, which is expressed in the Quadratic Equation Standard Form ax² + bx + c = 0. You will study various methods to solve these equations, including the Factorization Method, the method of Completing the Square, and the Quadratic Formula. Furthermore, you will learn how to determine the Nature of Roots of an equation using the discriminant (b² – 4ac), a concept that is extremely important for the CBSE Class 10 Maths Quiz and your board exams.

Conclusion

Mastery of quadratic equations comes not just from theoretical knowledge but from consistent practice. Our Class 10 Maths Chapter 4 Quadratic Equations MCQs Quiz is designed to make your practice effective and engaging. This quiz helps you strengthen your grip on important methods like Solving Quadratic Equations by Factorization and using the Quadratic Formula, providing practice in solving questions accurately under time pressure. By solving these objective questions, you can identify your weaknesses and gain the confidence to score full marks in this chapter. Take this Free Online Maths Quiz for Class 10 and excel!

FAQs

1. Question: How many marks from the chapter Quadratic Equations are asked in the board exam?
Answer: This chapter typically carries 7-8 marks in the CBSE board exam, with questions including MCQs, short answer, and long answer types.

2. Question: What is the standard form of a quadratic equation?
Answer: The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.

3. Question: What are the methods for solving quadratic equations?
Answer: The main methods are the factorization method, completing the square method, and using the quadratic formula.

4. Question: Which formula is used to determine the nature of the roots?
Answer: The value of the discriminant, D = b² – 4ac, is used to determine the nature of the roots of a quadratic equation.

5. Question: Is this Quadratic Equations quiz based on the NCERT syllabus?
Answer: Yes, our Quadratic Equations Class 10 quiz is fully based on the NCERT curriculum and the CBSE syllabus.

6. Question: If the discriminant of a quadratic equation is positive, what is the nature of its roots?
Answer: If the discriminant (D > 0) is positive, the equation has two distinct and real roots.

7. Question: Is this online quiz free?
Answer: Yes, this Free Online Maths Quiz for Class 10 is absolutely free. You can take it anytime and anywhere for practice.

8. Question: How should I prepare this chapter for the board exam?
Answer: First, understand all methods and formulas thoroughly. Then, solve the examples and exercise questions from the NCERT book. Finally, test your preparation with our Quadratic Equations Online Test.

9. Question: What is the quadratic formula?
Answer: For the equation ax² + bx + c = 0, the quadratic formula is x = [-b ± √(b² – 4ac)] / 2a.

10. Question: What is the benefit of taking this online quiz?
Answer: This quiz helps you improve time management, check the accuracy of your formulas, and understand the exam pattern, which boosts your confidence and leads to better performance.

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