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Varvara68 [4.7K]
3 years ago
10

Solve the equation for all real solutions in simplest form. z^2 - 12z +9= -3

Mathematics
1 answer:
Mars2501 [29]3 years ago
3 0

Answer:

Solving the equation for all real solutions in simplest form.

z^2 - 12z +9= -3 we get \mathbf{z=10.9\: or\: z=1.1}

Step-by-step explanation:

We need to solve the equation for all real solutions in simplest form.

z^2 - 12z +9= -3

First simplifying the equation:

z^2 - 12z +9+3= -3+3\\z^2 - 12z +12= 0

Now, we can solve the equation using quadratic formula:

z=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

we have a = 1, b=-12 and c=12

Putting values in formula and finding values of x

z=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\z=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(12)}}{2(1)}\\z=\frac{12\pm\sqrt{144-48}}{2}\\z=\frac{12\pm\sqrt{96}}{2}\\z=\frac{12\pm9.8}{2}\\z=\frac{12+9.8}{2}\:or\:z=\frac{12-9.8}{2}\\z=10.9\:or\:z=1.1

So, we get value of z: z=10.9 or z=1.1

Solving the equation for all real solutions in simplest form.

z^2 - 12z +9= -3 we get \mathbf{z=10.9\: or\: z=1.1}

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\mathrm{The\:mode\:is\:the\:term\:in\:the\:data\:set\:that\:appears\:the\:most.}

\mathrm{If\:there\:is\:more\:than\:one\:term\:that\:appears\:the\:most,\:then\:there\:is\:no\:mode.}

\mathrm{Count\:the\:number\:of\:times\:each\:element\:appears\:in\:the\:list}

\begin{pmatrix}148&160&191&212&246&262&264&268\\ 1&1&1&1&1&1&1&1\end{pmatrix}

\mathrm{The\:most\:common\:element\:is\:not\:unique,\:so\:there\:is\:no\:mode}

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