Question

Represent the following situations in the form of quadratic equations:

The product of two consecutive positive integers is 306. We need to find the integers
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Answer 1

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Let us consider,

The first integer number = x

Thus, the next consecutive positive integer will be = x + 1

Product of two consecutive integers

= x × (x +1) = 306

⇒ x^2 + x = 306

⇒ x^2 + x – 306 = 0

Therefore, the two integers x and x+1,

satisfies the quadratic equation, x^2 + x – 306 = 0,

which is the required representation of the problem mathematically.

Answer 2

The product of two consecutive positive integers is 306.

We need to find the integers

solution : Let two consecutive numbers are x and (x + 1)

A/C to question,

product of x and (x + 1) = 306

⇒x(x + 1) = 306

⇒x² + x - 306 = 0

⇒ x² + 18x - 17x - 306 = 0

⇒x(x + 18) - 17(x + 18) = 0

⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18

so x = 17 and (x +1) = 18

Therefore the numbers are 17 and 18.