Question

explaining the process of modeling and solving a quadratic equation
the product of two consecutive positive integers is 1,332.
explain how you can write and solve a quadratic
equation to find the value of the larger integer.

Explanation:

Answer:

Let the smaller integer be \(x\). Then the larger integer is \(x + 1\). The equation is \(x(x + 1)=1332\), which simplifies to \(x^{2}+x - 1332=0\). Factoring or using the quadratic formula \(x=\frac{-1\pm\sqrt{1 + 5328}}{2}=\frac{-1\pm73}{2}\). Since \(x\) is positive, \(x = 36\). The larger integer is \(37\).