NCERT Solutions For Class 10 Math Chapter – 4 Exercise – 4.4
Q1. Find the nature of the roots of the following quadratic equations. If the real roots exist , find them;
- 2x2– 3x + 5 = 0
- 3x2– 4√3x + 4 = 0
- 2x2– 6x + 3 = 0
Solution:-
- A = 2 , b=-3 and c = 5
Discriminant = b2– 4ac
= (-3)2 -4(2)(5)
= 9 – 40
= -31
As b2 – 4ac < 0
- A = 3 , b -4√3 and c = 4
Discriminant = b2 – 4ac
(-4√3)2 – 4(3)(4)
0
Real roots
- 2x2– 6x + 3 = 0
A = 2 , b = -6 and c = 3
Discriminant = b2 – 4ac
= (-6)2 – 4(2)(3)
= 36 – 24
= 12
Q2. Find the values of k for each of the following quadratic equations , so that they have two equal roots.
- 2x2+ kx + 3 = 0
- Kx (x-2) + 6 = 0
Solutions:-
- A = 2 , b = k and c= 3
Discriminant = b2 – 4ac
= (k)2 -4(2)(3)
= k2 – 24
For equal roots,
Discriminant = 0
K2 – 24 = 0
K2 = 24
K = +√24 = +2√6.
- Kx(x-2) + 6 = 0
A = k , b = -2k and c = 6
Discriminant = b2 – 4ac
= (-2k)2 – 4(k)(6)
= 4k2 – 24k
For equal roots,
B2– 4ac = 0
4k2 – 24k = 0
K = 0 or k = 6
Q3. Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is 800 m2 ? If so find its length and breadth .
Solution:-
A = 1 , b = 0 and c = 400
Discriminant = b2 – 4ac
= (0)2 – 4(1)(-400)
= 1600
Breadth of mango grove = 20 m.
Length of mango grove = 2 x 20 = 40 m.
Q4. 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:-
X2 – 20x + 112 = 0
A = 1 , b= -20 c = 112
Discriminant = b2 – 4ac
= (-20)2 – 4 x 112
= -48
Q5. Is it possible to design a rectangular park of perimeter 80 and area 400 m2 ? If so find its length and breadth.
Solution:-
L2 – 40l + 400 = 0
A = 1 , b = -40 c = 400
Discriminant = b2-4ac
(-40)2– 4 x 400
= 1600 – 1600
= 0
Root of this equation l = -b/2a
L = (40/2)
L = 20 m
B = 40 – l
40 – 20
= 20 m.