Then the number of marbles Rajendar had = 45 – x (Why?).
The number of marbles left with Sridhar, when he lost 5 marbles = x – 5
The number of marbles left with Rajendar, when he lost 5 marbles = (45 – x) – 5
= 40 – x
Therefore, their product = (x – 5) (40 – x)
= 40x – x
2
– 200 + 5x
= – x
2
+ 45x – 200
So, – x
2
+ 45x – 200 = 124 (Given that product = 124)
i.e.,– x
2
+ 45x – 324 = 0
i.e., x
2
– 45x + 324 = 0
(Multiply by -1)
Therefore, the number of marbles Sridhar had ‘x’, should satisfy the quadratic equation
x
2
– 45x + 324 = 0
which is the required representation of the problem.
ii. Let the length of smaller side be x cm
Then length of larger side = (x + 5) cm
Given length of hypotenuse = 25 cm
We know that in a right angle triangle (hypotenuse)2
= (side)2
+ (side)2
So, x
2
+ (x + 5)2
= (25)2
x
2
+ x
2
+ 10x + 25 = 625
2x
2
+ 10x - 600 = 0
x
2
+ 5x - 300 = 0
Value of x from the above equation will give the possible value of length of sides of the
given right angled triangle.
Example-2.
Check whether the following quadratic equations:
i. (x – 2)2
+ 1 = 2x – 3
ii. x(x + 1) + 8 = (x + 2) (x – 2)
iii. x (2x + 3) = x
2
+ 1
iv. (x + 2)3
= x
3
– 4
Solution : i. LHS = (x – 2)2
+ 1 = x
2
– 4x + 4 + 1 = x
2
– 4x + 5
Therefore, (x – 2)2
+ 1 = 2x – 3 can be written as
x
2
– 4x + 5 = 2x – 3
page no:108
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