Class 10 Maths Chapter 4 Quadratic Equations – Exercise 4.2 NCERT Solutions

Introduction

Exercise 4.2 focuses on solving quadratic equations using the factorization method. This method involves expressing the quadratic polynomial as a product of two linear factors and then equating each factor to zero to find the roots.

Formula Used

• General Form of Quadratic Equation:

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

• Factorization Method: Split the middle term (bx) into two terms such that their product = $a\cdot c$. Then factorize and solve.

NCERT Questions with Solutions (10)

Q1. Solve $x^2-5x+6=0$.

Solution: Factorize: $(x-2)(x-3)=0$. Roots: $x=2,3$.

Q2. Solve $x^2+7x+10=0$.

Solution: Factorize: $(x+5)(x+2)=0$. Roots: $x=-5,-2$.

Q3. Solve $x^2-4x-5=0$.

Solution: Factorize: $(x-5)(x+1)=0$. Roots: $x=5,-1$.

Q4. Solve $x^2+11x+24=0$.

Solution: Factorize: $(x+8)(x+3)=0$. Roots: $x=-8,-3$.

Q5. Solve $x^2-6x+9=0$.

Solution: Factorize: $(x-3)(x-3)=0$. Roots: $x=3,3$ (equal roots).

Q6. Solve $x^2+4x-12=0$.

Solution: Factorize: $(x+6)(x-2)=0$. Roots: $x=-6,2$.

Q7. Solve $x^2-7x+12=0$.

Solution: Factorize: $(x-3)(x-4)=0$. Roots: $x=3,4$.

Q8. Solve $x^2+9x+20=0$.

Solution: Factorize: $(x+5)(x+4)=0$. Roots: $x=-5,-4$.

Q9. Solve $x^2-10x+21=0$.

Solution: Factorize: $(x-7)(x-3)=0$. Roots: $x=7,3$.

Q10. Solve $x^2+6x+5=0$.

Solution: Factorize: $(x+5)(x+1)=0$. Roots: $x=-5,-1$.

FAQs (10 from NCERT)

1. Q: What is the factorization method? A: Splitting the middle term to factorize the quadratic polynomial.

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

3. Q: What is the condition for quadratic equation? A: $a\mathrm{\ne }0$.

4. Q: What are roots of a quadratic equation? A: Values of $x$ that satisfy the equation.

5. Q: What is meant by equal roots? A: When both roots are the same.

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

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

8. Q: Can factorization always be used? A: Only when quadratic can be factorized easily.

9. Q: What is the alternative method? A: Quadratic formula or completing the square.

10. Q: Why is this exercise important? A: It builds algebraic skills for solving quadratic equations.

Conclusion

Exercise 4.2 has 10 solved questions and 10 FAQs that strengthen your understanding of solving quadratic equations using the factorization method. This builds the foundation for advanced algebraic techniques in Class 10 Maths.

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