A hockey team is revealing their championship banner outside their stadium. The banner is in the shape of a triangle with a heig
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So, n = 3, is a 3rd degree polynomial, roots are -2 and 2i
well 2i is a complex root, or imaginary, and complex root never come all by their lonesome, their sister is always with them, the conjugate, so if 0+2i is there, 0-2i is there too
so, the roots are -2, 2i, -2i
now...![\bf \begin{cases} x=-2\implies x+2=0\implies &(x+2)=0\\ x=2i\implies x-2i=0\implies &(x-2i)=0\\ x=-2i\implies x+2i=0\implies &(x+2i)=0 \end{cases} \\\\\\ (x+2)\underline{(x-2i)(x+2i)}=0\\\\ -----------------------------\\\\ \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -----------------------------\\\\ (x+2)[x^2-(2i)^2]=0\implies (x+2)[x^2-(2^2i^2)]=0 \\\\\\ (x+2)[x^2-(4\cdot -1)]=0\implies (x+2)(x^2+4)=0 \\\\\\ x^3+2x^2+4x+8=0](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Ax%3D-2%5Cimplies%20x%2B2%3D0%5Cimplies%20%26%28x%2B2%29%3D0%5C%5C%0Ax%3D2i%5Cimplies%20x-2i%3D0%5Cimplies%20%26%28x-2i%29%3D0%5C%5C%0Ax%3D-2i%5Cimplies%20x%2B2i%3D0%5Cimplies%20%26%28x%2B2i%29%3D0%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A%28x%2B2%29%5Cunderline%7B%28x-2i%29%28x%2B2i%29%7D%3D0%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ctextit%7Bdifference%20of%20squares%7D%0A%5C%5C%20%5Cquad%20%5C%5C%0A%28a-b%29%28a%2Bb%29%20%3D%20a%5E2-b%5E2%5Cqquad%20%5Cqquad%20%0Aa%5E2-b%5E2%20%3D%20%28a-b%29%28a%2Bb%29%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%28x%2B2%29%5Bx%5E2-%282i%29%5E2%5D%3D0%5Cimplies%20%28x%2B2%29%5Bx%5E2-%282%5E2i%5E2%29%5D%3D0%0A%5C%5C%5C%5C%5C%5C%0A%28x%2B2%29%5Bx%5E2-%284%5Ccdot%20-1%29%5D%3D0%5Cimplies%20%28x%2B2%29%28x%5E2%2B4%29%3D0%0A%5C%5C%5C%5C%5C%5C%0Ax%5E3%2B2x%5E2%2B4x%2B8%3D0)
now, if we check f(-1), we end up with 5, not 15
hmmm
so, how to turn our 5 to 15? well, 3*5, thus
usually, when we get the roots, or zeros, if any common factor that is a constant is about, they get in a division with 0 and get tossed, and aren't part of the roots, thus, we can simply add one, in this case, the common factor of 3, to make the 5 turn to 15
well 2i is a complex root, or imaginary, and complex root never come all by their lonesome, their sister is always with them, the conjugate, so if 0+2i is there, 0-2i is there too
so, the roots are -2, 2i, -2i
now...
now, if we check f(-1), we end up with 5, not 15
hmmm
so, how to turn our 5 to 15? well, 3*5, thus
usually, when we get the roots, or zeros, if any common factor that is a constant is about, they get in a division with 0 and get tossed, and aren't part of the roots, thus, we can simply add one, in this case, the common factor of 3, to make the 5 turn to 15
Answer:
About 11.299 hours.
Step-by-step explanation:
To solve this problem, you can set up an equation to model the decay of the medicine. Let's call the time that medicine has been in the body x.
Taking the log x of both sides, you get
hours. Hope this helps!