Question

Erik and Caleb were trying to solve the equation: 0=(3x+2)(x-4) Erik said, "The right-hand side is factored, so I'll use the zero product property." Caleb said, "I'll multiply (3x+2)(x-4) and rewrite the equation as 0=3x^2-10x-8 Then I'll use the quadratic formula with a=3, b=-10, and c=-8. Whose solution strategy would work? A) Erik B) Caleb C) Both D) Neither

Answer 1

Both

Explanation:

Answer 2

C) Both

Explanation:

The given equation is:

`0=(3x+2)(x-4)`

To solve the given equation, we can use the Zero Product Property according to which if the product A.B = 0, then either A = 0 OR B = 0.

Using this property:

`(3x+2) = 0 \Rightarrow \bold{x = -(2)/(3)}\\(x-4) = 0 \Rightarrow \bold{x = 4}`

So, Erik's solution strategy would work.

Now, let us discuss about Caleb's solution strategy:

Multiply
`(3x+2)(x-4)` i.e.
`3x^2-12x+2x-8` =
`3x^2-10x-8`

So, the equation becomes:

`0=3x^2-10x-8`

Comparing this equation to standard quadratic equation:

`ax^2+bx+c=0`

a = 3, b = -10, c = -8

So, this can be solved using the quadratic formula.

`x=(-b\pm√(b^2-4ac))/(2a)`

`x=(-(-10)\pm√((-10)^2-4*3 * (-8)))/(2* 3)\\x=(-(-10)\pm√(196))/(6)\\x=(10\pm14)/(6) \\\Rightarrow x= 4, -(2)/(3)`

The answer is same from both the approaches.

So, the correct answer is:

C) Both