ML Aggarwal Quadratic Equations Chapter Test Class 9 ICSE Maths Solutions. Step by step solutions of Quadratic Equations as council prescribe guideline. Visit official website CISCE for detail information about ICSE Board Class-9.

## ML Aggarwal Quadratic Equations Chapter Test Class 9 ICSE Maths Solutions

Board | ICSE |

Subject | Maths |

Class | 9th |

Chapter-7 | Quadratic Equations |

Topics | Solution of Ch-Test Questions |

Academic Session | 2024-2025 |

### Solution of Ch-Test Questions on Quadratic Equations

ML Aggarwal Quadratic Equations Chapter Test Class 9 ICSE Maths Solutions

**Question 1.**** **

**(i) x (2x + 5) = 3**

**(ii) 3x ^{2} – 4x – 4 = 0.**

**Answer:**

**(i) x (2x + 5) = 3**

We can write it as

2x^{2} + 5x – 3 = 0

By further calculation

2x^{2} + 6x – x – 3 = 0

By taking out the common terms

2x (x + 3) – 1 (x + 3) = 0

So we get

(x + 3) (2x – 1) = 0

Here

x + 3 = 0 then x = – 3

2x – 1 = 0 then 2x = 1 where x = ½

Therefore, x = – 3, ½.

**(ii) 3x**^{2} – 4x – 4 = 0

^{2}– 4x – 4 = 0

We can write it as

3x^{2} – 6x + 2x – 4 = 0

By taking out the common terms

3x (x – 2) + 2 (x – 2) = 0

So we get

(x – 2) (3x + 2) = 0

Here

x – 2 = 0 then x = 2

3x + 2 = 0 then 3x = – 2 where x = – 2/3

Therefore, x = 2, – 2/3.

**Question 2.**** **

**(i) 4x ^{2} – 2x + ¼ = 0**

**(ii) 2x ^{2} + 7x + 6 = 0.**

**Answer:**

**(i) 4x**^{2} – 2x + ¼ = 0

^{2}– 2x + ¼ = 0

Multiply the equation by 4

16x^{2} – 8x + 1 = 0

We can write it as

16x^{2} – 4x – 4x + 1 = 0

Taking out the common terms

4x (4x – 1) – 1 (4x – 1) = 0

So we get

(4x – 1) (4x – 1) = 0

(4x – 1)^{2} = 0

Here

4x – 1 = 0

4x = 1

By division

x = ¼, ¼

**(ii) 2x**^{2} + 7x + 6 = 0

^{2}+ 7x + 6 = 0

We can write it as

2x^{2} + 4x + 3x + 6 = 0

By further calculation

2x (x + 2) + 3 (x + 2) = 0

So we get

(x + 2) (2x + 3) = 0

Here

x + 2 = 0 then x = – 2

2x + 3 = 0 then 2x = – 3 where x = – 3/2

x = – 2, – 3/2

**Question 3.**** **

**(i) (x – 1)/ (x – 2) + (x – 3)/ (x – 4) = 3 1/3**

**(ii) 6/x – 2/(x – 1) = 1/(x – 2).**

**Answer:**

**(i) (x – 1)/ (x – 2) + (x – 3)/ (x – 4) = 3 1/3**

By taking LCM

[(x – 1) (x – 4) + (x – 2) (x – 3)]/ (x – 2) (x – 4) = 10/3

By further calculation

(x^{2} – 5x + 4 + x^{2} – 5x + 6)/ (x^{2} – 6x + 8) = 10/3

So we get

(2x^{2} – 10x + 10)/ (x^{2} – 6x + 8) = 10/3

By cross multiplication

10x^{2} – 60x + 80 = 6x^{2} – 30x + 30

By further simplification

10x^{2} – 60x + 80 – 6x^{2} + 30x – 30 = 0

So we get

4x^{2} – 30x + 50 = 0

Dividing by 2

2x^{2} – 15x + 25 = 0

It can be written as

2x^{2} – 10x – 5x + 25 = 0

Taking out the common terms

2x (x – 5) – 5 (x – 5) = 0

(x – 5) (2x – 5) = 0

Here

x – 5 = 0 then x = 5

2x – 5 = 0 then 2x = 5 where x = 5/2

Therefore, x = 5, 5/2.

**(ii) 6/x – 2/(x – 1) = 1/(x – 2)**

Taking LCM

(6x – 6 – 2x)/ x (x – 1) = 1/ (x – 2)

By further calculation

(4x – 6)/ (x^{2} – x) = 1/(x – 2)

By cross multiplication

4x^{2} – 8x – 6x + 12 = x^{2} – x

So we get

4x^{2} – 14x + 12 – x^{2} + x = 0

3x^{2} – 13x + 12 = 0

3x^{2} – 4x – 9x + 12 = 0

Taking out the common terms

x (3x – 4) – 3 (3x – 4) = 0

(3x – 4) (x – 3) = 0

Here

3x – 4 = 0 then 3x = 4 where x = 4/3

x – 3 = 0 then x = 3

Therefore, x = 3, 4/3.

— : End of ML Aggarwal Quadratic Equations Chapter Test Class 9 ICSE Maths Solutions :–

Return to :- ** ML Aggarawal Maths Solutions for ICSE Class-9**

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