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sveticcg [70]
3 years ago
12

Simplify this equation.

Mathematics
1 answer:
lakkis [162]3 years ago
4 0

Answer:

The simplified equation is \pm\frac{\sqrt{b^2-4ac}}{2a}

Step-by-step explanation:

Step 1:Applying Quotient Rule

\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0

\pm \sqrt{\frac{b^2-4ac}{4a^2}} = \pm \frac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}----------------------------(1)

Step 2:  Applying radical Rule

\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0

\sqrt{4a^2}=\sqrt{4}\sqrt{a^2}

So equation(1) can be written as

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

Now

\sqrt{4} = 2

\sqrt{a^2} = a

Now equation(2) becomes

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

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