Exam Question:

The product of two consecutive positive integers is 306. Form the quadratic equation to find x, if x denotes the smaller integer.

Answer:

For IBDP Mathematics, you should know:

The smallest positive integer should be x.

As a result, (x + 1) is the next positive integer that is greater than x.

The sum of two consecutive positive integers is now known to be 306.

Create the quadratic equation first, then.

⇒x(x+1)=306

The simplified version of the equation is x^2+x-306=0.

So, this quadratic equation must be solved.

Factorize the following equation: x^2+18x-17x-306=0.

Now that we have simplified the equation above, we have x(x+18)-17(x+18)=0.

⇒(x+18)(x−17)=0

⇒(x+18)=0, (x−17)=0

⇒x=17,−18

Thus, 17 is the positive integer.

Consequently, the product of two consecutive positive integers 17 and (17 + 1 = 18) is 306.

To conclude, 17 is the smallest positive integer.

Work hard for your IBDP Mathematics examination!

End of analysis. Great!