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.(1 point)

Answer 1

To translate the given statement into a quadratic equation, we need to identify the variable in question (let's use \( x \) to represent "the number").

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

Next, "plus the product of five and the same number" translates to:
\[
5x
\]

Putting it all together, the equation reads:
\[
-6x^2 + 5x = 31
\]

To express this as a standard quadratic equation (set to zero), we can rearrange it as follows:
\[
-6x^2 + 5x - 31 = 0
\]

Thus, the quadratic equation equivalent to the given statement is:
\[
-6x^2 + 5x - 31 = 0
\]