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Questions
Represent the following situation in the form of a quadratic equation:
The product of two consecutive positive integers is 306. We need to find the integers.
The product of two consecutive positive integers is 306. Find the integers.
Solution
Let the first integer number = x
Next consecutive positive integer will = x + 1
Product of both integers = x × (x +1) = 306
⇒ x2 + x = 306
⇒ x2 + x - 306 = 0
⇒ 2x2 + 18x - 17x - 306 = 0
⇒ x(x + 18) - 17(x + 18) = 0
⇒ (x + 18)(x - 17) = 0
⇒ x + 18 = 0 and x - 17 = 0
⇒ x = -18 and x = 17
Since,
First positive integer = x = 17
Second positive integer = x + 1
= 17 + 1
= 18
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