Question

select the quadratic equation that is equivalent to the product of negative six and a number squared plus the product of five and the same number is thirty one

Answer 1

To create the quadratic equation based on the given statement, we will first assign a variable to represent "the number." Let's use \( x \).

According to the problem, we have:

1. "The product of negative six and a number squared" can be expressed as:
\[
-6x^2
\]

2. "The product of five and the same number" can be written as:
\[
5x
\]

3. And this entire expression is equal to thirty-one:
\[
-6x^2 + 5x = 31
\]

Now, to write this as a standard quadratic equation, we will rearrange it:

\[
-6x^2 + 5x - 31 = 0
\]

For a cleaner look, we can also multiply the entire equation by -1 (although it doesn't change the solutions) to make the leading coefficient positive:

\[
6x^2 - 5x + 31 = 0
\]

Thus, the quadratic equation that is equivalent to the problem statement is:

\[
6x^2 - 5x - 31 = 0
\]