SOLUTION: Help What type of solution do you get for quadratic equations where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation.

Question 41299This question is from textbook
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What type of solution do you get for quadratic equations where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation. This question is from textbook

Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
By D you meant determinant. Right?

For a quadratic equation with real coefficients, if D < 0 then the roots are imaginery and occur in conjugate pairs as well.
Thus if be a quadratic equation where a,b,c are real then if then the roots are of the form A + iB and A - iB where A and B are real.

Example: is a quadratic equation with real coefficients.
The determinant is = 64 - 100 = -36 < 0.
Now let us find the roots.
Sreedharachary's formula is

or
or
or =
Thus either x = -0.8 + 0.6i or x = -0.8 - 0.6i

So you can see that the roots are complex conjugate.
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