Hello students, we are providing assertion reason questions for class 10. Assertion Reason questions are the new question format that is introduced in CBSE board. The resources for assertion reason questions are very less. So, to help students we have created chapterwise assertion reason questions for class 10 maths. In this article, you will find assertion reason questions for CBSE Class 10 Maths Chapter 4 Quadratic Equations. It is a part of Assertion Reason Questions for CBSE Class 10 Maths Series.
| Chapter | Quadratic Equations |
| Type of Questions | Assertion Reason Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 10 |
| Subject | Maths |
| Useful for | Class 10 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 10 Maths Chapterwise Assertion Reason |
Assertion Reason Questions on Quadratic Equations
Assertion and Reason Questions
Directions: Each of the following questions consists of two statements: an Assertion (A) and a Reason (R). Answer them by selecting the correct option:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
Q1. Assertion (A): The equation $x^2-2 x+1=0$ has two equal real roots.
Reason (R): The discriminant of the equation is zero.
Answer: Option (a) is correct.
Explanation: The discriminant $D=b^2-4 a c=4-4=0$. This means the equation has real and equal roots.
Difficulty Level: Easy
Q2. Assertion (A): The quadratic equation $x^2+4 x+5=0$ has real roots.
Reason (R): The discriminant is greater than zero.
Answer: Option (c) is correct.
Explanation: Here, $D=16-20=-4$, which is negative, so the roots are complex (non-real). A is false and $R$ is also false.
Difficulty Level: Moderate
Q3. Assertion (A): If the product of the roots of a quadratic equation is positive and the sum is negative, then both roots are negative.
Reason (R): The product of roots is $\frac{c}{a}$, and the sum is $-\frac{b}{a}$.
Answer: Option (a) is correct.
Explanation: If the product is positive and sum is negative, then both roots must be negative numbers.
Difficulty Level: Moderate
Q4. Assertion (A): The quadratic equation $2 x^2-4 x+3=0$ has two distinct real roots.
Reason (R): If $D<0$, the roots are imaginary.
Answer: Option (d) is correct.
Explanation: $D=(-4)^2-4 \times 2 \times 3=16-24=-8$, so the roots are imaginary, not real and distinct. $A$ is false, $R$ is true.
Difficulty Level: Tough
Q5. Assertion (A): The roots of the quadratic equation $a x^2+b x+c=0$ are given by the quadratic formula
$$
x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}
$$
Reason (R): The formula is derived using the method of completing the square.
Answer: Option (a) is correct.
Explanation: This is the standard derivation of the quadratic formula using completing the square technique.
Difficulty Level: Easy
Also check
- Some Applications of Trigonometry Class 10 Assertion Reason Questions Maths Chapter 9
- Introduction to Trigonometry Class 10 Assertion Reason Questions Maths Chapter 8
- Coordinate Geometry Class 10 Assertion Reason Questions Maths Chapter 7
- Triangles Class 10 Assertion Reason Questions Maths Chapter 6
- Arithmetic Progressions Class 10 Assertion Reason Questions Maths Chapter 5
- Quadratic Equations Class 10 Assertion Reason Questions Maths Chapter 4
- Pair of Linear Equations in Two Variables Class 10 Assertion Reason Questions Maths Chapter 3
- Polynomials Class 10 Assertion Reason Questions Maths Chapter 2
- Real Numbers Class 10 Assertion Reason Questions Maths Chapter 1
Topics from which assertion reason questions may be asked
- Standard Form
- Factorization and Quadratic Formula
- Nature of Roots
Quadratic equations often model situations of area, motion, and finance.
Assertion reason questions from the above given topic may be asked.
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Frequently Asked Questions (FAQs) on Quadratic Equations Assertion Reason Questions Class 10
Q1: What does the chapter ‘Quadratic Equations’ cover?
A1: It builds key concepts related to quadratic equations and prepares you for logical reasoning-based questions.
Q2: What are assertion reason questions?
A2: These consist of two statements: an assertion and a reason. Students need to determine their correctness and relationship.
Q3: Why practice assertion reason questions in Quadratic Equations?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from quadratic equations.
Q4: Are assertion reason questions part of CBSE board exams?
A4: Yes, they are included under competency-based formats to test depth of understanding.
