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Solutions of Problems Involving Quadratic Equation
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Here you'll learn about some problems of real world application of quadratic equations. First step is to formulate a quadratic equation whose solution is a solution of the given problem. There may be a chance that one of the roots of quadratic equation only have meaning. In such a case the roots which do not satisfy the condition will not be considered.

Follow the following algorithm.
Step I: Translate the word problem into symbolic language and formulate the quadratic equation.
Step II: Solve the quadratic equation formed in Step I.
Step III: Translate the solution into verbal language and reject the solution which does not have a meaning for the problem.

Following example will illustrate the above procedure.
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Example: The sum of the squares of two consecutive natural numbers is 313. Find the numbers.
Solution: Let two consecutive natural numbers be x and x + 1.
Then, x2 + (x + 1)2 = 313 [Given]
2x2 + 2x + 1 = 313
2x2 + 2x - 312 = 0
x2 + x - 156 = 0
x2 + 13x - 12x - 156 = 0
x(x + 13) - 12(x + 13) = 0
(x + 13) (x - 12) = 0
x + 13 = 0 or x - 12 = 0
x = 12 or x = -13
Since x, being a natural number cannot be negative. Therefore, x = 12.
Hence, the two consecutive natural numbers are 12 and 13.
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