Question

the product of two consecutive integers is 342. which quadratic equation can be used to find x, the greater number?
○ $x^2 + 1 = 342$
○ $x^2 - 1 = 342$
○ $x^2 - x + 342 = 0$
○ $x^2 - x - 342 = 0$

Explanation:

Step1: Define the consecutive integers

Let the greater integer be \( x \). Then the smaller consecutive integer is \( x - 1 \) (since consecutive integers differ by 1).

Step2: Set up the product equation

The product of the two consecutive integers is 342, so we have the equation:
\( x(x - 1) = 342 \)

Step3: Expand and rearrange the equation

Expanding the left - hand side: \( x^{2}-x = 342 \)
Subtract 342 from both sides to get the quadratic equation in standard form (\( ax^{2}+bx + c = 0 \)):
\( x^{2}-x - 342=0 \)

Answer:

\( x^{2}-x - 342 = 0 \) (the fourth option: \( x^{2}-x - 342 = 0 \))