Class 10 Maths Chapter 4 Quadratic Equations – Exercise 4.1 NCERT Solutions

Introduction

Exercise 4.1 introduces quadratic equations and how they arise in real‑life situations. A quadratic equation is an equation of the form:

$$a{x}^2+bx+c=0,a\mathrm{\ne }0$$

This exercise focuses on identifying quadratic equations from given expressions and word problems.

Formula Used

• General Form of Quadratic Equation:

$$a{x}^2+bx+c=0$$

• Condition: $a\mathrm{\ne }0$.

NCERT Questions with Solutions (10)

Q1. Check whether $x^2+2x+1=0$ is a quadratic equation.

Solution: Yes, it is in the form $a{x}^2+bx+c=0$.

Q2. Check whether $2x^2-3=0$ is a quadratic equation.

Solution: Yes, $a=2,b=0,c=-3$.

Q3. Check whether $x^3+2x^2+1=0$ is a quadratic equation.

Solution: No, it is cubic (degree 3).

Q4. Check whether $2x^2+3x=0$ is a quadratic equation.

Solution: Yes, $a=2,b=3,c=0$.

Q5. Check whether $x^2-5x+6=0$ is a quadratic equation.

Solution: Yes, $a=1,b=-5,c=6$.

Q6. Check whether $x^4+2x^2+1=0$ is a quadratic equation.

Solution: No, it is quartic (degree 4).

Q7. Check whether $3x^2+7=0$ is a quadratic equation.

Solution: Yes, $a=3,b=0,c=7$.

Q8. Check whether $x^2+\frac{1}{x}=0$ is a quadratic equation.

Solution: No, because it contains $\frac{1}{x}$.

Q9. Check whether $2x^2-4x+8=0$ is a quadratic equation.

Solution: Yes, $a=2,b=-4,c=8$.

Q10. Check whether $x^2+2x+3=5$ is a quadratic equation.

Solution: Rearrange: $x^2+2x-2=0$. Yes, quadratic.

FAQs (10 from NCERT)

1. Q: What is a quadratic equation? A: An equation of the form $a{x}^2+bx+c=0$.

2. Q: What is the degree of a quadratic equation? A: Degree = 2.

3. Q: Can quadratic equations have real solutions? A: Yes, depending on discriminant.

4. Q: What is the discriminant? A: $D=b^2-4ac$.

5. Q: What does discriminant tell us? A: Nature of roots (real, equal, or complex).

6. Q: What is a cubic equation? A: Equation of degree 3.

7. Q: What is a quartic equation? A: Equation of degree 4.

8. Q: What is the condition for quadratic equation? A: Coefficient of $x^2$ must be non‑zero.

9. Q: Can quadratic equations be solved graphically? A: Yes, by plotting parabola.

10. Q: Why is this exercise important? A: It helps identify quadratic equations and prepares for solving them.

Conclusion

Exercise 4.1 has 10 solved questions and 10 FAQs that strengthen your understanding of quadratic equations and their identification. This builds the foundation for solving quadratic equations in Class 10 Maths.

Visit: www.fuzymathacademy.com