Question

Dimitri and Jillian were trying to solve the equation:(x + 1)(x + 3) = 12Dimitri said, "The left-hand side is factored, so I'll use the zero product property."Jillian said, "I'll multiply (x + 1)(x + 3) and rewrite the equation as x^2 + 4x + 3 = 12. Then I'll solveusing the quadratic formula with a = 1, b = 4, and c = 3."Whose solution strategy would work?Choose 1 answer: A) Only Dimitri'sB) Only Julian'sC) BothD) Neither

Answer 1

Let's begin by identifying key information given to us:

$\mleft(x+1\mright)\mleft(x+3\mright)=12$

Dimitri's Method

$\begin{gathered} \mleft(x+1\mright)\mleft(x+3\mright)=12 \\ \Rightarrow x+1=12,x+3=12 \\ x=12-1=11,x=12-3=9 \\ \therefore x=11,x=9 \end{gathered}$

Jilian's Method

$\begin{gathered} \mleft(x+1\mright)\mleft(x+3\mright)=12 \\ x^2+4x+3=12 \\ a=1,b=4,c=3 \\ We\text{ use the quadratic formula, we have:} \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-4\pm\sqrt[]{4^2-4(1)(3)}}{2(1)}=\frac{-4\pm\sqrt[]{16-12}}{2} \\ x=\frac{-4\pm\sqrt[]{4}}{2}=\frac{-4\pm2}{2} \\ x=\frac{-4-2}{2},\frac{-4+2}{2} \\ x=-\frac{6}{2},-\frac{2}{2} \\ x=-3,-1 \end{gathered}$

The Proper Method

$\begin{gathered} \mleft(x+1\mright)\mleft(x+3\mright)=12 \\ x^2+4x+3=12\Rightarrow x^2+4x+3-12=0 \\ x^2+4x+3-12=0\Rightarrow x^2+4x-9=0 \\ x^2+4x-9=0 \\ a=1,b=4,c=-9 \\ We\text{ will use the quadratic formula to solve, we have:} \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-4\pm\sqrt[]{4^2-4(1)(-9)}}{2(1)}=\frac{-4\pm\sqrt[]{16+36}}{2} \\ x=\frac{-4\pm\sqrt[]{52}}{2} \\ x=\frac{-4+\sqrt[]{52}}{2}\text{.}\frac{-4-\sqrt[]{52}}{2} \end{gathered}$

Both Dimitri & Julian were wrong in their strategy

strategyAs such Neither of their soluiton stratefy would work