NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 10 |

Subject |
Maths |

Chapter |
Chapter 4 |

Chapter Name |
Quadratic Equations |

Exercise |
Ex 4.4 |

Number of Questions Solved |
5 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4

**Question 1.
**

**Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:**

(i) 2x² -3x + 5 = 0

(ii) 3x

^{2}– 4√3x + 4 = 0

(iii) 2x

^{2}-6x + 3 = 0

**Solution:**

**(i) 2x**

^{2}– 3x + 5 = 0This is of the form ax

^{2}+ bx + c = 0,

where a = 2, b = -3 and c = 5

Discriminant, D = b

^{2}-4ac

= (-3)

^{2}-4 x 2 x 5 = 9 – 40 = -31

Since, D < 0

Hence, no real roots exist.

**(ii) 3x ^{2} – 4√3x + 4 = 0**

**(iii) 2x**

^{2}-6x + 3 = 0**Question 2.
**

**Find the values of k for each of the following quadratic equations, so that they have two equal roots.**

**(1) 2x**

^{2}+ kx + 3 = 0**(2) kx (x – 2) + 6 = 0**

**Solution:**

**Question 3.
**

**Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m**

^{2}? If so, find its length and breadth.**Solution:**

Let breadth of the rectangular mango grove be x m

Then, the length of rectangular mango grove be 2xm

According to question,

x x 2x = 800

⇒ 2x

^{2}= 800

⇒ x

^{2}= 400

⇒ x = ±20 [-20 is rejected]

Hence, breadth = 20 m and length = 2 x 20 = 40 m

So, it is possible to design a rectangular mango grove whose length is twice its breadth.

**Question 4.
**

**Is the following situation possible? If so, determine their present ages.**

**The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.**

**Solution:**

Let the present age of one friend be x years

Then, the present age of other friend be (20 -x) years

4 years ago, one friend’s age was (x – 4) years

4 years ago, other friend’s age was (20 -x – 4) = (16 -x) years

According to question,

(x-4) (16-x) = 48

⇒ 16x – x

^{2}– 64 + 4x = 48

⇒ x

^{2}– 20x + 112 = 0

This is of the form ax

^{2}+ bx + c = 0, where, a = 1, b = -20 and c = 112

Discriminant, D = b

^{2}– 4ac

= (-20)

^{2}– 4 x 1 x 112 = 400 – 448 = – 48 < 0

Since, no real roots exist.

So, the given situation is not possible.

**Question 5.
**

**Is it possible to design a rectangular park of perimeter 80 m and area 400 m**

^{2}? If so, find its length and breadth.**Solution:**

Let the length of rectangular park be x m and breadth be y m.

**Given:**area = 400 m

^{2}

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