Question

Represent the following situation in the from of quadratic equations: The product of two consecutive positive integers ia 306.we need to find the integers

Answer 1

Let two consecutive positive integers are x and (x + 1) .

a/c to question, The product of two consecutive positive integers is 306.

e.g., x × (x + 1) = 306

=> x² + x - 306 = 0

hence, x² + x - 306 = 0 is the form of quadratic equation.

now, x² + x - 306 = 0

=> x² + 18x - 17x - 306 = 0

=> x(x + 18) - 17(x + 18) = 0

=> (x - 17)(x + 18) = 0

=> x = -18 and 17 but x ≠ -18 because x is positive integer.

so, x = 17 and x + 1 = 18

therefore, two positive integers are 17 and 18

Answer 2

Answer:

EQUATION :

x² + x - 306 = 0

SOLUTIONS :

17, 18

Step-by-step explanation:

Let,

the integers be 'x' and 'x+1'.

Given,

their product = 306

(x)(x + 1) = 306

x² + x - 306 = 0

Solving the equation :

x² + x - 306 = 0

x² + 18x - 17x - 306 = 0

x(x + 18) - 17 (x + 18) = 0

(x + 18)(x - 17) = 0

x = -18

x = 17

Here, in the question, they have given that it is a positive integer.

So, we have to consider x = 17

If one positive integer is 17, then the other is 18.

Therefore, the integers are 17 and 18.

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