SOLUTION: 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 and find the solution of

Question 170775This question is from textbook
: 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 and find the solution of the equation.
I have tried three times and still I am wrong, please help. This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If , then the quadratic will have two complex (ie non real) solutions.

Why? Recall that the quadratic formula is

The discriminant D is everything in the square root. So this means that

Now if , this means that "D" is negative. Remember you CANNOT take the square root of a negative number. This is why you will NOT get any real solutions if

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For example, let's find the discriminant for

From we can see that , , and

Start with the discriminant formula

Plug in , , and

Square to get

Multiply to get

Subtract from to get

Since the discriminant is less than zero, this means that there are two complex solutions

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Now let's use the quadratic formula to find the solutions of

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Simplify to get . Note:

or Break up the expression.

or Break up the fraction for each case.

or Reduce.

So our answers are or

Since our answers are complex (ie not real), this verifies our original claim.

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