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Practice Class 10 Maths Chapter 4 Quadratic Equations MCQ Questions with Answers based on the latest NCERT syllabus. Solve fresh, board exam-oriented MCQs on standard form, roots, factorisation, discriminant, quadratic formula, and nature of roots with detailed solutions.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Quadratic Equations
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 1
Difficulty Level: Easy to Moderate
Based On: NCERT Latest Syllabus
Introduction
The chapter Quadratic Equations introduces students to equations in which the highest power of the variable is 2. Students learn different methods to solve quadratic equations and find their roots.
This chapter covers important concepts such as factorisation, completing the square, quadratic formula, discriminant, and the nature of roots. These concepts are important for Class 10 board examinations and also provide a strong foundation for higher-level mathematics.
What You Will Learn?
✔ Standard form of a quadratic equation
✔ Identification of quadratic equations
✔ Roots of a quadratic equation
✔ Factorisation method
✔ Completing the square
✔ Quadratic formula
✔ Discriminant
✔ Nature of roots
✔ Applications of quadratic equations
Why This Topic Is Important?
Quadratic Equations is an important chapter in Class 10 Mathematics. Questions can be asked directly from formulas as well as through application-based problems.
A good understanding of this chapter helps students solve problems involving roots, equations, dimensions, numbers, and other mathematical situations.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Mathematics Practice Tests
Q1. Which of the following is a quadratic equation?
A) $$2x+5=0$$
B) $$x^2-7x+10=0$$
C) $$3x-2=0$$
D) $$5x+1=2x+4$$
Answer:
B) $$x^2-7x+10=0$$
Useful Concept
The standard form of a quadratic equation is:
$$ax^2+bx+c=0,\quad a\ne0$$
The highest power of the variable must be 2.
Solution
Consider option B:
$$x^2-7x+10=0$$
Here, the highest power of $$x$$ is 2.
Therefore, it is a quadratic equation.
The other options are linear equations because their highest power of the variable is 1.
Hence, the correct answer is:
B) $$x^2-7x+10=0$$
Q2. What are the roots of the equation?
$$x^2-5x+6=0$$
A) $$(1,6)$$
B) $$(2,3)$$
C) $$(-2,-3)$$
D) $$(3,4)$$
Answer:
B) $$(2,3)$$
Useful Concept
For factorisation, we look for two numbers whose:
Product = $$c$$
and
Sum = $$b$$
For the equation:
$$x^2-5x+6=0$$
we need two numbers whose product is 6 and sum is -5.
Those numbers are -2 and -3.
Solution
Given:
$$x^2-5x+6=0$$
Split the middle term:
$$x^2-2x-3x+6=0$$
Take common factors:
$$x(x-2)-3(x-2)=0$$
Therefore:
$$(x-2)(x-3)=0$$
Using the zero product property:
$$x-2=0$$
or
$$x-3=0$$
Therefore:
$$x=2$$
or
$$x=3$$
Hence, the roots are:
$$2,\ 3$$
Therefore, the correct answer is:
B) $$(2,3)$$
Q3. For the quadratic equation
$$2x^2+7x+3=0$$
what is the value of $$a$$ in the standard form $$ax^2+bx+c=0$$?
A) $$2$$
B) $$7$$
C) $$3$$
D) $$1$$
Answer:
A) $$2$$
Useful Concept
The standard form of a quadratic equation is:
$$ax^2+bx+c=0$$
Here:
$$a=$$ coefficient of $$x^2$$
$$b=$$ coefficient of $$x$$
$$c=$$ constant term
Solution
Given:
$$2x^2+7x+3=0$$
Comparing it with:
$$ax^2+bx+c=0$$
we get:
$$a=2$$
$$b=7$$
$$c=3$$
Therefore:
$$a=2$$
Hence, the correct answer is:
A) $$2$$
Q4. What is the discriminant of the quadratic equation?
$$x^2-6x+5=0$$
A) $$4$$
B) $$16$$
C) $$36$$
D) $$56$$
Answer:
B) $$16$$
Useful Formula
For the quadratic equation:
$$ax^2+bx+c=0$$
the discriminant is:
$$D=b^2-4ac$$
Solution
Given:
$$x^2-6x+5=0$$
Therefore:
$$a=1$$
$$b=-6$$
$$c=5$$
Using:
$$D=b^2-4ac$$
Substituting the values:
$$D=(-6)^2-4(1)(5)$$
$$D=36-20$$
$$D=16$$
Hence, the correct answer is:
B) $$16$$
Q5. Which condition represents two distinct real roots of a quadratic equation?
A) $$D<0$$
B) $$D=0$$
C) $$D>0$$
D) $$D\leq0$$
Answer:
C) $$D>0$$
Useful Concept
The discriminant of a quadratic equation is:
$$D=b^2-4ac$$
The value of $$D$$ determines the nature of the roots.
Solution
If:
$$D>0$$
then the quadratic equation has two distinct real roots.
If:
$$D=0$$
then the equation has two equal real roots.
If:
$$D<0$$
then the equation has no real roots.
Therefore, the condition for two distinct real roots is:
$$D>0$$
Hence, the correct answer is:
C) $$D>0$$
Important Formulas & Concepts
Standard Form
$$ax^2+bx+c=0,\quad a\ne0$$
Quadratic Formula
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
Discriminant
$$D=b^2-4ac$$
Nature of Roots
If:
$$D>0$$
The equation has two distinct real roots.
If:
$$D=0$$
The equation has two equal real roots.
If:
$$D<0$$
The equation has no real roots.
Sum of Roots
If the roots are $$\alpha$$ and $$\beta$$:
$$\alpha+\beta=-\frac{b}{a}$$
Product of Roots
$$\alpha\beta=\frac{c}{a}$$
Related Practice Questions
Try solving the following questions yourself:
Q1. Find the roots of:
$$x^2-9x+20=0$$
Q2. Find the discriminant of:
$$3x^2-4x+1=0$$
Q3. Identify $$a$$, $$b$$ and $$c$$ in:
$$5x^2-2x-3=0$$
Q4. What is the nature of roots when:
$$D=0$$
Q5. Write the quadratic formula for:
$$ax^2+bx+c=0$$
Mini Quiz Challenge
Try to answer these questions within 60 seconds.
Q1. What is the highest power of the variable in a quadratic equation?
Q2. What is the formula for the discriminant?
Q3. What does $$D=0$$ indicate?
Q4. What is the product of roots of $$ax^2+bx+c=0$$?
Q5. What is the standard form of a quadratic equation?
Challenge: Try to answer all five questions without looking at your notes.
Exam Tips
✔ Always convert the equation into standard form before applying a formula.
✔ Carefully identify the values of $$a$$, $$b$$ and $$c$$.
✔ Pay special attention to the sign of $$b$$.
✔ Remember the discriminant formula:
$$D=b^2-4ac$$
✔ Do not forget the $$\pm$$ sign in the quadratic formula.
✔ Verify your roots whenever possible.
✔ Show proper calculation steps in board examinations.
Quick Revision Notes
✔ A quadratic equation has degree 2.
✔ Its standard form is $$ax^2+bx+c=0$$, where $$a\ne0$$.
✔ The discriminant is $$D=b^2-4ac$$.
✔ $$D>0$$ gives two distinct real roots.
✔ $$D=0$$ gives two equal real roots.
✔ $$D<0$$ gives no real roots.
✔ Quadratic equations can be solved using factorisation, completing the square, and the quadratic formula.
✔ Sum of roots is $$-\frac{b}{a}$$.
✔ Product of roots is $$\frac{c}{a}$$.
Common Mistakes Students Make
❌ Forgetting to write the equation in standard form.
❌ Identifying $$a$$, $$b$$ and $$c$$ incorrectly.
❌ Ignoring the negative sign of $$b$$.
❌ Writing $$b^2-4ac$$ incorrectly.
❌ Making sign errors while using the quadratic formula.
❌ Forgetting the $$\pm$$ sign.
❌ Not checking the obtained roots.
Key Takeaways
✔ A quadratic equation has the highest degree 2.
✔ The standard form is $$ax^2+bx+c=0$$.
✔ Factorisation can be used to find roots when the equation can be easily factorised.
✔ The quadratic formula can be used for any quadratic equation.
✔ The discriminant determines the nature of roots.
✔ Correct identification of $$a$$, $$b$$ and $$c$$ is essential for accurate calculations.
FAQs
Q. What is a quadratic equation?
Answer:
An equation whose highest power of the variable is 2 is called a quadratic equation.
Its standard form is:
$$ax^2+bx+c=0,\quad a\ne0$$
Q. What is the discriminant?
Answer:
The discriminant is given by:
$$D=b^2-4ac$$
It helps determine the nature of the roots of a quadratic equation.
Q. When does a quadratic equation have two distinct real roots?
Answer:
A quadratic equation has two distinct real roots when:
$$D>0$$
Q. When are the roots equal?
Answer:
The roots are equal when:
$$D=0$$
Q. Which methods can be used to solve quadratic equations?
Answer:
Quadratic equations can be solved using factorisation, completing the square, and the quadratic formula.
Conclusion
These Class 10 Maths Chapter 4 Quadratic Equations MCQ Questions with Answers and Solutions – provide fresh, NCERT-based practice on standard form, roots, factorisation, discriminant, and the nature of roots.
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