## Exercise 4.3 class 10 maths

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

(i) 2xÂ² – 3x + 5 =0

Here a = 2 , b = -3 , c = 5

D = bÂ² – 4ac

D = (-3)Â² – 4 Ã— 2 Ã— 5

D = 9 – 40

D = – 31

Since D < 0 so there is no real roots exist.

(ii) 3xÂ² – 4âˆš3 x + 4 = 0

Here a = 3 , b = -4âˆš3 , c = 4

D = bÂ² – 4ac

D = (-4âˆš3)Â² – 4 Ã— 3 Ã— 4

D = 48 – 48

D = 0

Since D = 0 so it has 2 real and equal roots exist.

Using quadratic formula

(iii) 2xÂ² – 6x + 3 = 0

Here a= 2 , b = -6 , c = 3

D = bÂ²- 4ac

D = (-6)Â² – 4 Ã— 2 Ã— 3

D = 36 – 24

D = 12

Since D > 0 so it has 2 real and distinct roots exits.

Using Quadratic formula

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

(i) 2xÂ² + kx + 3 = 0

Here a = 2 , b = k , c = 3

Since it has 2 equal roots

So D = 0

bÂ² – 4ac = 0

kÂ² – 4Ã— 2 Ã— 3 = 0

kÂ² -24= 0

kÂ² = 24

k = âˆš24

k = 2âˆš6 or k = – 2âˆš6

(ii) kx (x – 2) + 6 = 0

kxÂ² – 2kx +6 = 0

Here a = k , b = -2k. , c = 6

Since it has 2 equal roots so

D = 0

bÂ² – 4ac = 0

(-2k)Â² – 4Ã— kÃ— 6 = 0

4kÂ² -24k = 0

4k ( k – 6 ) = 0

Either 4k = 0 so k =0 but it doesn’t satisfy the equation so rejected.

Or k-6= 0 then k= 6 ans.

**3. Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 mÂ² ? if so, find its length and breadth**.

Solutions: Let length be x m so breadth will be 2x m.

Area of rectangular grove = 800 mÂ²

x (2x) =800

2xÂ² -800 = 0

Here a = 2, b = 0 and c = 800

Discriminant (D) = bÂ² – 4ac

D = 0Â² – 4 Ã— 2 Ã— 800

D = – 6400

Since D < 0 so this quadratic equation has no real roots exist. Hence this is not possible to design such rectangular mango grove.

**4. Is the following situation possible ? if so, determine their present ages the sum of the ages of two friends is 20 years 4 years ago the product of their ages in years was 48.**

Solution: let present age of first friend be x years

and present age of second friend be (20 – x) years

four years age of first friend = (x- 4)yrs

and age of second friend =(20 – x-4)yrs

= (16-x)yrs

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

16x -xÂ²-64 +4x =48

xÂ² -20 x +112 = 0

Here a = 1 , b = -20 , c = 112

D = bÂ²- 4ac

D = (-20)Â²-4Ã—1Ã—112

D = 400 – 448

D = -48

Since D <0 so no real roots exist. Therefore the given situation is not possible.

**5. Is it possible to design a rectangular park of perimeter 80 meter and area 400 m square if so find its length and breadth.**

Solution: Let length be x m and breadth be y m

perimeter of rectangular park = 80m

2( x + y) = 80

x+y = 40

y = 40 – x ……….(i)

Area of rectangular park= 400mÂ²

x Ã— y = 400

Using equation (i)

x ( 40 – x) =400

40x – xÂ² = 400

xÂ² – 40x + 400 =0

Here a = 1 , b = -40 , c = 400

Discriminant (D) = bÂ²-4ac

D = (-40)Â² – 4 Ã— 1 Ã—400

D = 1600 – 1600

D = 0. Since D = 0 so this quadratic equation has 2 real and equal roots exist.do this is possible to design such rectangular park.

Using quadratic formula

x = -b/2a, -b/2a

x = – (-40)/2 , -(-40)/2

x = 20, 20. Put x= 20 in (i)

y = 20

So length and breadth are 20m , 20m

Ncert Solutions Class 10 Maths Exercise 1.1 https://10thmathsguide.com/exercise-11-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 1.2

Ncert Solutions Class 10 Maths Exercise 2.1 https://10thmathsguide.com/exercise-21-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 2.2

Ncert Solutions Class 10 Maths Exercise 3.1 https://10thmathsguide.com/exercise-31-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.2 https://10thmathsguide.com/exercise-32-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.3 https://10thmathsguide.com/exercise-33-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.1 https://10thmathsguide.com/exercise-41-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.2 https://10thmathsguide.com/exercise-42-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.3 https://10thmathsguide.com/exercise-43-class-10-maths/

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**MCQ Questions for Class 10 Maths all Chapters****https://sharmatutorial.in/category/mcq-class-10-maths/**