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Quadratic Equations

Question

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O Girl! Out of a group of swans, $space 7 over 2$ times the square root of the number are playing on the shore of a tank. The two remaining ones are playing, with amorous fight, in the water. What is the total number of swans?

Solution

Let the total number of swans be x. Then, Number of swans playing on the shore of the tank

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Remaining swans = 2
Now,
∴

straight x equals 7 over 2 square root of straight x plus 2

rightwards double arrow

straight x minus 7 over 2 square root of straight x minus 2 equals 0

Let

space space space square root of straight x space equals space 4

∴

straight x equals straight y squared

rightwards double arrow

straight y squared minus 7 over 2 straight y minus 2 equals 0 comma

where

straight y squared equals straight x

rightwards double arrow

2 straight y squared minus 7 straight y minus 4 equals 0

rightwards double arrow

2 straight y squared minus 8 straight y plus straight y minus 4 equals 0

rightwards double arrow

2 straight y left parenthesis straight y minus 4 right parenthesis space plus space left parenthesis straight y minus 4 right parenthesis space space equals space 0

rightwards double arrow

left parenthesis straight y minus 4 right parenthesis space left parenthesis 2 straight y plus 1 right parenthesis space space equals space 0

rightwards double arrow

straight y equals 4 space or space straight y space equals space minus 1 half

rightwards double arrow

straight y equals 4

rightwards double arrow

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rightwards double arrow

straight x equals 16.

Hence, the total number of swans is 16.

Some More Questions From Quadratic Equations Chapter

Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem situations in the form of quadratic equations:
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Find the roots of the following quadratic equations by factorisation method:
x² – 3x – 10 = 0

Find the roots of the following quadratic equations by factorisation method:
2x² + x – 6 = 0

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.

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