IBDP Mathematics Question Analysis Topic: Mathematics -
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!
