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makkiz [27]
1 year ago
14

Example Solve the quadratic equation x² - 6x +13=0

Mathematics
1 answer:
EastWind [94]1 year ago
8 0

x^2-6x+13=0\\\\\implies x^2-6x =-13\\\\\implies x^2 -2\cdot 3 \cdot x+3^2 -3^2 =-13\\\\\implies (x-3)^2 -9 = -13\\\\\implies (x-3)^2 = -13 +9 = -4\\\\ \implies x-3 =\pm\sqrt{-4} \\\\\implies x -3 = \pm2i\\\\\implies x = \pm 2i +3\\\\\text{Hence,}~ x = 3 + 2i, ~~  x = 3-2i

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Please help ASAP<br><br> If f(x) = x^2-6x+2 and g(x) =sqrt x find a.) (fog) (x)<br> b.) (gof) (-2)
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\large\begin{array}{l} \left\{\!\begin{array}{l} \mathsf{f(x)=x^2-6x+2}\\ \mathsf{g(x)=\sqrt{x}}\\ \end{array}\right. \end{array}


\large\begin{array}{l} \textsf{a) }\mathsf{(f\circ g)(x)}\\\\ =\mathsf{f\big[g(x)\big]}\\\\ =\mathsf{\big[g(x)\big]^2-6\cdot g(x)+2}\\\\ =\mathsf{\big[\sqrt{x}\big]^2-6\sqrt{x}+2}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{(f\circ g)(x)=x-6\sqrt{x}+2} \end{array}}\qquad\checkmark \end{array}

______


\large\begin{array}{l} \textsf{b) }\mathsf{(g\circ f)(-2)}\\\\ =\mathsf{g\big[f(-2)\big]}\\\\ =\mathsf{\sqrt{f(-2)}}\\\\ =\mathsf{\sqrt{(-2)^2-6\cdot (-2)+2}}\\\\ =\mathsf{\sqrt{4+12+2}}\\\\ =\mathsf{\sqrt{18}}\\\\ =\mathsf{\sqrt{3^2\cdot 2}}\\\\ =\mathsf{3\sqrt{2}}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{(g\circ f)(-2)=3\sqrt{2}} \end{array}}\qquad\checkmark \end{array}

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If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2181559


\large\textsf{I hope this helps. :-)}


Tags: <em>composite function composition evaluate algebra</em>

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