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Formulate the quadratic equation: Sum of two numbers is 27 and the product is 182.
Let one number be x, then the other one will be 27 − x.
Product = 182 x(27 - x) = 182 27x − x2 = 182 x2 − 27x + 182 = 0
Formulate the quadratic equation:
Two consecutive integers whose sum of squares is 182.
Let the two consecutive integers be x and x + 1.
So
x2 + (x + 1)2 = 182 x2 + x2 + 2x + 1 = 182 2x2 + 2x - 181 = 0
The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth.
Let the breadth be xm, then the length will be 2x + 1 m.
Area = x(2x + 1) = 528 2x2 + x - 528 = 0
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