Question

Simplify this equation.

Answer 1

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

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