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Exercise 4.4
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Q.2 (i) For what values of k the quadratic equation 2x + kx +3 = 0 has equal roots?

2
Ans. For equal roots, D = b - 4ac = 0
2
k - 4(2)(3) = 0
2
k - 24 = 0

Q.3: Is it possible to design a rectangle mango grove whose length is twice its breadth
2
and the area is 800 m . If so, find its length and Breadth

Ans: let the breadth of the mango grove be x m.
then, length = 2x
2
It is given that area of rectangular mango grove is 800 m .
(2x)x = 800
2
2x =800
2
x = 400
2
x - 400 = 0
here a = 1, b = 0 c = - 400
2
D = b - 4ac
2
= (0) - 4(1)(-400)
= 1600 > 0 since D > 0, therefore, it is possible to design a rectangular mango grove
with the given conditions.

Now
x = 20 or x = -20
Reject x = - 20 as a cannot be negative.
breadth = 20 m
and length = 2x = 2 20 = 40 m

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