The Product of Two Consecutive Positive Integers is 306
Question:
The product of two consecutive positive integers is 306. Form the quadratic equation to find the integers, if \(x\) denotes the smaller integer.
Solution
Let the smaller positive integer be
\[ x \]
Then the next consecutive positive integer is
\[ x+1 \]
According to the question,
\[ x(x+1)=306 \]
Expanding,
\[ x^2+x=306 \]
Bringing all terms to one side,
\[ x^2+x-306=0 \]
Required Quadratic Equation
\[ \boxed{x^2+x-306=0} \]
This is the quadratic equation whose solutions give the required consecutive positive integers.
Answer
If \(x\) denotes the smaller integer, then the required quadratic equation is
\[ \boxed{x^2+x-306=0} \]