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 th

Question 149395: 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.
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
----------------
By "D" I assume mean the discriminant, b^2-4ac.
If D<0 the quadratic equation will produce two
solutions that are both complex numbers because
you will be taking the square root of a negative
in the process.
---------------------------
Example:
y = x^2-x+4
D = b^2-4ac = 1-4*1*4 = -15
---------
Solutions:
x = [1 +- sqrt(-15)]/2
x = [1 + isqrt(15)]/2 or x = [1- i sqrt(15)]/2
==========================
Cheers,
Stan H.
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.

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

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 .

Take the square root of to get .

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, this verifies our original claim.

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