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.

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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) About Me  (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 ax%5E2+%2B+bx+%2B+c+=+0 be a quadratic equation where a,b,c are real then if b%5E2-4%2Aa%2Ac+%3C0 then the roots are of the form A + iB and A - iB where A and B are real.

Example: 5x%5E2+%2B+8x+%2B+5+=+0 is a quadratic equation with real coefficients.
The determinant is 8%5E2+-+4%2A5%2A5 = 64 - 100 = -36 < 0.
Now let us find the roots.
Sreedharachary's formula is
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
or x+=+%28-8+%2B-+sqrt%28+-36+%29%29%2F10+
or x+=+%28-8+%2B-+sqrt%28+%286%2Ai%29%5E2+%29%29%2F10+
or x+=+%28-8+%2B-+6%2Ai%29%2F10+ = -0.8+%2B-+0.6%2Ai+
Thus either x = -0.8 + 0.6i or x = -0.8 - 0.6i

So you can see that the roots are complex conjugate.