SOLUTION: Please help. 1. If x = 1 and x = -8, then form a quadratic equation. I have no idea where to even begin an equation. 2. What type of solution do you get for quadratic equations

Question 149605: Please help.
1. If x = 1 and x = -8, then form a quadratic equation. I have no idea where to even begin an equation.
2. 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.
Iknow if discriminant is less than zero no solutions are defined. But I don't know how to explain why or how to begin an example. Please explain and keep it as simplistic as possible so that I can understand. Like if you were explaining it to a 9 year old.
Thank you so much for all your time and help!!!!!

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

Start with the given zeros

and

Get all terms to the left side in each case (ie subtract 1 from both sides in the first equation and add 8 to both sides in the second equation)

and

Now use the zero product property in reverse to join the factors.

FOIL and multiply

-------------------------------------------
Answer:

So the polynomial with zeros of and is

Notice how if we graph , we can see that the polynomial has roots of and

Graph of with roots of and

# 2

Remember the quadratic formula is

Where the discriminant is . So the quadratic formula could also look like

If D<0, then we'll be taking the square root of a negative number (which we cannot do). So this results in 2 complex solutions (ie no 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 (or no real 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 (non real), this verifies our original claim.

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