Question

Which two equations would be most appropriately solved by using the zero product property?

Select each correct answer.




3x^2−6x=0

0.25x^2+0.8x−8=0

−(x−1)(x+9)=0

4x² = 13

Answer 1

Answers are

3x^2−6x=0

−(x−1)(x+9)=0

Explanation:

Zero product property: Whenever you get an equation of the form
`a\cdot b \cdot ... = 0` (basically factors multiplying together to equal 0) then the equation will be satisfied if at least one of the factors is equal to zero. It's because zero times anything is equal to zero.

`3x^2-6x = 0` is easily factorable to use the zero product property.If we factor out
`3x`, we get

`3x(x - 2) = 0`

and we can easily see that
`x=0` or
`x=2` are solutions because both numbers will make the entire left side of the equation equal to 0.

Anything multiplied by 0 is zero; if
`x=0` or
`(x-2) = 0`, equation will be satisfied.

From

`-(x-1)(x+9) = 0`

it is clear that solutions are
`x=1` and
`x=-9`.

The other choices are not as easy to factor (maybe not even factorable).