SOLUTION: i need to use the discriminant to determine the number of solutions of this quadratic equation, and whether the solutions are real or complex. i have to find the roots, but i do h

Question 144574: i need to use the discriminant to determine the number of solutions of this quadratic equation, and whether the solutions are real or complex. i have to find the roots, but i do have to determine the number and types of solutions. x2 + 6x - 7 = 0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the discriminant formula

Plug in a=1, b=6, c=-7

Square 6 to get 36

Multiply -4*1*-7 to get 28

Combine 36 and 28 to get 64

Since the discriminant equals 64 (which is greater than zero) , this means there are two real solutions.

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=6, and c=-7

Square 6 to get 36

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

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