Answer:
C) Both
Step-by-step explanation:
The given equation is:
[tex]0=(3x+2)(x-4)[/tex]
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:
[tex](3x+2) = 0 \Rightarrow \bold{x = -\frac{2}{3}}\\(x-4) = 0 \Rightarrow \bold{x = 4}[/tex]
So, Erik's solution strategy would work.
Now, let us discuss about Caleb's solution strategy:
Multiply [tex](3x+2)(x-4)[/tex] i.e. [tex]3x^2-12x+2x-8[/tex] = [tex]3x^2-10x-8[/tex]
So, the equation becomes:
[tex]0=3x^2-10x-8[/tex]
Comparing this equation to standard quadratic equation:
[tex]ax^2+bx+c=0[/tex]
a = 3, b = -10, c = -8
So, this can be solved using the quadratic formula.
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-(-10)\pm\sqrt{(-10)^2-4\times3 \times (-8)}}{2\times 3}\\x=\dfrac{-(-10)\pm\sqrt{196}}{6}\\x=\dfrac{10\pm14}{6} \\\Rightarrow x= 4, -\dfrac{2}{3}[/tex]
The answer is same from both the approaches.
So, the correct answer is:
C) Both
