Access answers to NCERT Class 10 Maths Chapter 4 - Quadratic Equations

 Access answers to NCERT Class 10 Maths Chapter 4 - Quadratic Equations

Exercise 4.1 Page: 73

1. Check whether the following are quadratic equations:

(i) (x + 1)² = 2(x-3)

(ii) x2 - 2x = (-2) (3 - x)

(iii) (x-2)(x + 1) = (x - 1)(x + 3)

(iv) (x - 3) (2x+1) = x(x + 5)

(v) (2x - 1)(x-3) = (x + 5)(x - 1)

(vi) x2 + 3x + 1 = (x - 2)2

(vii) (x + 2)3 = 2x (x² - 1)

(viii) x³ - 4x2 - x + 1 = (x - x³- - 2)3

Solutions:

(i) Given,

(x + 1)² = 2(x-3) By using the formula for (a+b)² = a²+2ab+b² x²+2x + 1 = 2x - 6 ⇒ x² + 7 = 0

The above equation is in the form of ax2 + bx + c = 0

Therefore, the given equation is a quadratic equation. 

(ii) Given, x2 - 2x = (-2) (3 - x) x²-2x = -6 + 2x ⇒ x2 - 4x + 6 = 0

The above equation is in the form of ax2 + bx + c = 0

Therefore, the given equation is a quadratic equation.

(iii) Given, (x - 2)(x+1)=(x-1)(x + 3)

By multiplication,

x²-x-2= x² + 2x - 3

⇒ 3x-1=0

The above equation is not in the form of ax2 + bx + c = 0

Therefore, the given equation is not a quadratic equation.

(iv) Given, (x - 3) (2x+1) = x(x + 5)

By multiplication,

2x25x-3 = x² + 5x

x²-10x-3=0

The above equation is in the form of ax2 + bx + c = 0

Therefore, the given equation is a quadratic equation.

(v) Given, (2x - 1)(x-3) = (x + 5) (x - 1) -

By multiplication, ⇒ 2x27x + 3 = x² + 4x - 5 x²-11x + 8 = 0

The above equation is in the form of ax2 + bx + c = 0.

Therefore, the given equation is a quadratic equation.

(vi) Given, x² + 3x + 1 = (x - 2)2

By using the formula for (a-b)²= a²-2ab+b² ⇒ x2 + 3x + 1 = x² + 4 - 4x

7x-3= 0

The above equation is not in the form of ax2 + bx + c = 0

Therefore, the given equation is not a quadratic equation.

(vii) Given, (x + 2)3 = 2x(x² - 1)

By using the formula for (a+b)³ = a³+b³+3ab(a+b)

⇒ x³ + 8 + x2 + 12x = 2x3 - 2x

⇒ x3 + 14x6x2 - 8 = 0

The above equation is not in the form of ax2 + bx + c = 0

Therefore, the given equation is not a quadratic equation.

(viii) Given, x³ - 4x2 - x + 1 = (x - 2)3

12:51 p.m.

By using the formula for (a-b)³ = a³-b³- 3ab(a-b)

x34x2 - x + 1 = x3-8-6x2 + 12x

⇒ 2x2-13x + 9 = 0

The above equation is in the form of ax2 + bx + c = 0

Therefore, the given equation is a quadratic equation. 

Solutions are given by Experts.