To find the quadratic equation suitable for determining [tex]\( x \)[/tex], the lesser number, you should follow these steps:
1. Define the two consecutive integers. Let the lesser number be [tex]\( x \)[/tex]. Hence, the next consecutive integer will be [tex]\( x + 1 \)[/tex].
2. Write down the product of these two integers. According to the given information, the product of these two integers is 420. Therefore:
[tex]\[
x \cdot (x + 1) = 420
\][/tex]
3. Expand the left-hand side of the equation:
[tex]\[
x^2 + x = 420
\][/tex]
We can now see that the equation [tex]\( x^2 + x = 420 \)[/tex] is the quadratic equation that can be used to find [tex]\( x \)[/tex].
Therefore, the correct quadratic equation is:
[tex]\[
x^2 + x = 420
\][/tex]
So, the answer is:
[tex]\[
x^2 + x = 420
\][/tex]
