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Let two consecutive positive integers are x and (x + 1). Then x(x + 1) = 306 ⇒ x 2 + x – 306 = 0 which is a quadratic equation in x. Solving this equation by factorisation method, we get x 2 + 18x – 17x – 306 = 0 ⇒ x(x + 18) – 17(x + 18) = 0 ⇒ (x + 18) (x – 17) = 0 ⇒ x + 18 = 0 or x – 17 = 0 ⇒ x = –18 or x = 17 But integers are +ve ∴ x = 17 Hence, two consecutive positive integers are 17 and 18.

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Quadratic Equations

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Short Answer Type

10. 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.

Let two consecutive positive integers are x and (x + 1). Then
x(x + 1) = 306
⇒ x² + x – 306 = 0
which is a quadratic equation in x.
Solving this equation by factorisation method, we get
x² + 18x – 17x – 306 = 0
⇒ x(x + 18) – 17(x + 18) = 0
⇒ (x + 18) (x – 17) = 0
⇒ x + 18 = 0 or x – 17 = 0
⇒ x = –18 or x = 17
But integers are +ve
∴ x = 17
Hence, two consecutive positive integers are 17 and 18.