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Question
If an integer is added to its square the sum is 90. Find the integer with the help of a quadratic equation.
Solution
Let the required integer be x.
Then according to the given condition
⇒ x + x2 = 90
⇒ x2 + x - 90 = 0
⇒ x2 + 10x - 9x - 90 = 0
⇒ x(x + 10) - 9(x +10) = 0
⇒ (x +10) (x - 9) = 0
⇒ x + 10 = 0 or x - 9 = 0
⇒ x = -10 or x = 9
Hence, the required integer is 9 or -10.
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