Question

question 5(multiple choice worth 1 points) (06.04 mc) a conference room is in the shape of a rectangle. its floor has a length of (x - 4) meters and a width of (3x - 1) meters: (x - 4)(3x - 1) which of the following simplified expressions represents the area of the floor of the conference room in square meters? x² - 13x + 4 3x² - 13x + 4 3x² - 11x + 4 x² - 12x + 4 question 6(multiple choice worth 1 points) (08.01 mc) what are the zeroes of f(x)=x² - x - 2? x=-2,1 x = 2,-1 x=-2,-1 x = 2,1

Explanation:

Step1: Expand the area formula

The area $A$ of a rectangle is $A = l\times w$, where $l=(x - 4)$ and $w=(3x - 1)$. Using the FOIL method: $(x - 4)(3x - 1)=x\times(3x)+x\times(- 1)+(-4)\times(3x)+(-4)\times(-1)=3x^{2}-x - 12x + 4$.

Step2: Combine like - terms

$3x^{2}-x - 12x + 4=3x^{2}-13x + 4$.

Step3: Find the zeros of the quadratic function

For $f(x)=x^{2}-x - 2$, we set $f(x) = 0$, so $x^{2}-x - 2=0$. Factor the quadratic equation: $x^{2}-x - 2=(x - 2)(x+1)=0$.

Step4: Solve for $x$

If $(x - 2)(x + 1)=0$, then $x-2=0$ or $x + 1=0$. So $x=2$ or $x=-1$.

Answer:

Question 5: $3x^{2}-13x + 4$
Question 6: $x = 2,-1$