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

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1 has all the solutions to the questions provided in the NCERT Book of the latest edition.

Students are advised to practice all the questions to get good marks in the board examination.

Textbook | NCERT |

Class | 10 |

Subject | Maths |

Chapter | 4 |

Exercise | 4.1 |

Chapter Name | Quadratic Equations |

## Class 10 Maths Chapter 4 Exercise 4.1 Quadratic Equations NCERT Solution

Check whether the following are quadratic equations :

(i) $$(x + 1)^{2}$$ = 2(x β 3)

Answer

$$x^{2}+2x+1 = 2x-3$$

$$x^{2}+2=0$$

Yes, it is Quadratic equations

(ii) $$x^{2} β 2x = (β2) (3 β x)$$

Answer

$$x^{2}-2x = -6+2x$$

$$x^{2}-4x+6=0$$

Yes, it is Quadratic equations

(iii) (x β 2)(x + 1) = (x β 1)(x + 3)

Answer

$$x^{2}-x-2 = x^{2}+2x-3$$

$$3x-1=0$$

No, it is not Quadratic equations because not in the form $$ax^{2}+ bx + c = 0$$

(iv) (x β 3)(2x +1) = x(x + 5)

Answer

$$2x^{2}-5x-3 = x^{2}+5x$$

$$x^{2}-10x-3=0$$

Yes, it is Quadratic equations

(v) (2x β 1)(x β 3) = (x + 5)(x β 1)

Answer

$$2x^{2}-7x+3 = x^{2}+4x-5$$

$$x^{2}-11x+8=0$$

Yes, it is Quadratic equations

(vi) $$x^{2} + 3x + 1 = (x β 2)^{2}$$

Answer

$$x^{2}+ 3x + 1 = x^{2}+4-4x$$

$$7x-3=0$$

No, it is not Quadratic equations because not in the form $$ax^{2}+ bx + c = 0$$

(vii) $$(x + 2)^{3} = 2x (x^{2} β 1)$$

Answer

$$x^{3}+8+6x^{2}+12x = 2x^{3}-2x$$

$$x^{3}-6x^{2}-14x-8=0$$

No, it is not Quadratic equations because not in the form $$ax^{2}+ bx + c = 0$$

(viii) $$x^{3} β 4x^{2} β x + 1 = (x β 2)^{3}$$

Answer

$$x^{3}-4x^{2}-x+1 = x^{3}-8-6x^{2}+12x$$

$$2x^{2}-13x+9=0$$

Yes, it is Quadratic equations

Represent the following situations in the form of quadratic equations :

(i) The area of a rectangular plot is 528 m2 . The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Answer

Let the breadth of plot be x

A/Q, length of plot = 2x + 1

and

Area of plot = 528

β $$(2x+1)x$$ = 528

β $$2x^{2}+x-528=0$$

(ii) The product of two consecutive positive integers is 306. We need to find the integers.

Answer

Let the smaller no. be x

then the larger no. = $$x+1$$

A/Q,

$$x(x+1)=306$$

β $$x^{2}+x-306=0$$

(iii) Rohanβs mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohanβs present age.

Answer

Let present age of Rohan be x year

then present age of Rohan’s mother = (x + 26) year

After 3 years

Age of Rohan = x + 3

Age of Rohan’s mother = $$x+26+3=x+29$$

A/Q,

$$(x+3)(x+29)=360$$

β $$x^{2}+32x+87=360$$

β $$x^{2}+32x-273=0$$

(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Answer

Let the speed of train be x km/hr

then the time taken(t) = $$\frac{480}{x}hr$$

A/Q,

t + 3 = $$\frac{480}{x-8}$$ $$\because t=\frac{d}{s}$$

β $$\frac{480}{x}+3=\frac{480}{x-8}$$

β $$3=480\left[\frac{1}{x-8}-\frac{1}{x}\right]$$

β $$1=160\left[\frac{x-(x-8)}{x(x-8)}\right]$$

β $$x^{2}-8x=160\times8$$

β $$x^{2}-8x-1280=0$$

Hope NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1, helps you in solving problems. If you have any doubts, drop a comment below and we will get back to you.