How do you solve 4w^2+100=0 using the quadratic formula?

1 Answer
flamespirit919
Apr 27, 2017

There are no real solutions.
w=-5i
w=5i

Explanation:

The quadratic formula is as follows
\frac{-b\pm\sqrt{b^2-4ac}}{2a}
Given a function in the form
aw^2+bw+c=0

Plugging in the values we have, we the following
\frac{-(0)+\sqrt{(0)^2-4(4)(100)}}{2(4)}
\frac{-(0)-\sqrt{(0)^2-4(4)(100)}}{2(4)}

Solving for the first one we get
\frac{\sqrt{0-1600}}{8}=\frac{\sqrt{-1600}}{8}

Solving for the second one we get
\frac{-\sqrt{0-1600}}{8}=\frac{-\sqrt{-1600}}{8}

There are no real solutions, but we can get the imaginary/complex solutions
\frac{\sqrt{1600\cdot -1}}{8}=\frac{40i}{8}=5i
\frac{-\sqrt{1600\cdot -1}}{8}=\frac{-40i}{8}=-5i

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