Quadratic Equations Class 10 Maths Exercise 4.1 PDF

Here you will find quadratic equations class 10 maths exercise 4.1 pdf solutions with a complete explanation. You can download the ex 4.1 class 10 solutions.

Ex 4.1 Class 10 Maths

1. Check whether the following are quadratic equations

(i). `(x+1)^2=2(x-3)` (ii). `x^2-2x=(-2)(3-x)` (iii). `\left(x-2\right)\left(x-1\right)=\left(x-1\right)\left(x=3\right)` (iv). `\left(x-3\right)\left(2x+1\right)=x\left(x+5\right)` (v). `\left(2x-1\right)\left(x-3\right)=\left(x+5\right)\left(x-1\right)` (vi). `x^2+3x+1=\left(x-2\right)^2` (vii). `(x+2)^3=2x(x^2-1)` (viii). `x^2-4x^2-x+1=(x-2)^3`

Class 10 Maths Ex 4.1 Solutions

Ex 4.1 class 10 Question i Solution 

The given equation is 

`(x+1)^2=2(x-3)` 

`\Rightarrow x^2+2x+1=2x-6` 

`\Rightarrow x^2+2x+1-2x+6=0` 

`\Rightarrow x^2+7=0` 

`\Rightarrow1.x^2+0.x+7=0`

It is of the form `{ab}^2+bx+c=0,\ where\ a\ne0`

Hence, the given equation is a quadratic equation. 

 Ex 4.1 class 10 Question  ii Solution 

The given equation is 

`x^2-2x=(-2)(3-x)` 

`\Rightarrow x^2-2x=-6+2x` 

`\Rightarrow x^2-2x-2x+6=0` 

`\Rightarrow x^2-4x+6=0` 

 `\Rightarrow{1.x}^2+\left(-4\right).x+6=0`

It is of the form `ab^2+bx+c=0,\ where\ a\ne0`

Hence, the given equation is a quadratic equation. 

 

Ex 4.1 class 10 Question iii Solution 

The given equation is 

`\left(x-2\right)\left(x-1\right)=\left(x-1\right)\left(x=3\right)` 

`\Rightarrow x^2+x-2x-2=x^2+3x-x-3` 

`\Rightarrow x^2-x-2=x^2+2x-3` 

`\Rightarrow x^2-x-2-x^2-2x+3=0` 

`\Rightarrow-3x+1=0` 

`\Rightarrow{0.x}^2+\left(-3\right).x+1=0` 

`\because a=0` 

It is of the form `ab^2+bx+c=0,\ where\ a\ne0`

Hence, the given equation is a quadratic equation. 

Ex 4.1 class 10 Question iv Solution 

the given equation is

`\left(x-3\right)\left(2x+1\right)=x\left(x+5\right)`  

`\Rightarrow2x^2+x-6x-3=x^2+5x` 

`\Rightarrow2x^2-5x-3=x^2+5x` 

`\Rightarrow2x^2-5x-3-x^2-5x=0` 

`\Rightarrow x^2-10x-3=0`

`\Rightarrow1.x^2+\left(-10\right).x+(-3)=0` 

It is of the form `ab^2+bx+c=0,\ where\ a\ne0`

Hence, the given equation is a quadratic equation. 

Ex 4.1 class 10 Question v Solution 

The  given equation is 

`\left(2x-1\right)\left(x-3\right)=\left(x+5\right)\left(x-1\right)` 

`\Rightarrow2x^2-6x-x+3=x^2-x+5x-5` 

`\Rightarrow2x^2-7x+3=x^2+4x-5` 

`\Rightarrow2x^2-7x+3-x^2-4x+5=0` 

`\Rightarrow x^2-11x+8=0`

`\Rightarrow1.x^2+\left(-11\right).x+8=0` 

It is of the form `ab^2+bx+c=0,\ where\ a\ne0`

Hence, the given equation is a quadratic equation. 

Ex 4.1 class 10 Question vi Solution

The given equation is 

`x^2+3x+1=\left(x-2\right)^2` 

`\Rightarrow x^2+3x+1=x^2-4x+4` 

`\Rightarrow x^2+3x+1-x^2+4x-4=0` 

`\Rightarrow7x-3=0`

`\Rightarrow0.x^2+7.x+(-3)=0` 

`\Rightarrow\because a=0` 

It is not of the form `ab^2+bx+c=0`,

Hence, the given equation is not a quadratic equation. 

Ex 4.1 class 10 Question vii Solution

The given equation is 

`(x+2)^3=2x(x^2-1)` 

`\Rightarrow x^3+6x^2+12x+8=2x^3-2x` 

`\Rightarrow x^3+6x^2+12x+8-2x^3+2x=0` 

`\Rightarrow-x^3+6x^2+14x+8=0` 

It is not of the form `ab^2+bx+c=0`,

Hence, the given equation is not a quadratic equation. 

Ex 4.1 class 10 Question viii Solution

The given equation is 

`x^2-4x^2-x+1=(x-2)^3` 

`\Rightarrow x^3-4x^2-x+1=x^3-6x^2+12x-8`

`\Rightarrow x^3-4x^2-x+1-x^3+6x^2-12x+8=0`

`\Rightarrow2x^2-13x+9=0` 

`\Rightarrow2.x^2+\left(-13\right).x+9=0` 

It is  of the form `ab^2+bx+c=0`,

Hence, the given equation is a quadratic equation. 

Hoping this Quadratic Equations Class 10 Maths Exercise 4.1 PDF will help you a lot.