Nature of Roots of Quadratic Equation:
CBSE Ncert Solutions Chapter 4 Quadratic Equations Exercise 4.4 Question 5
5. Is it possible to design a rectangular park of perimeter
metres and area
. If so, find its length and breadth.
Solution:
Let length of park =
metres
We are given area of rectangular park =
Therefore, breadth of park =
metres {Area of rectangle = length
}
Perimeter of rectangular park =
metres
We are given perimeter of rectangle =
metres
Therefore, we can write
Comparing equation,
with general quadratic equation
, we get
and
.
Discriminant is equal to 0. Therefore, two roots of equation are real and equal which means that it is possible to design a rectangular park of perimeter 80 metres and area
.
Using quadratic formula
to solve equation, we get
Here, both the roots are equal to
.
Therefore, length of rectangular park =
metres
Breadth of rectangular park =
metres
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