SOLUTION: Can anyone help me with this one? It requires me to determine the number of solutions and classify the type of solutions for each of the following equations? Justify the answer ple

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Can anyone help me with this one? It requires me to determine the number of solutions and classify the type of solutions for each of the following equations? Justify the answer ple      Log On


   

Question 199573: Can anyone help me with this one? It requires me to determine the number of solutions and classify the type of solutions for each of the following equations? Justify the answer please?
x^2-4x-77=0
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

From x%5E2-4x-77 we can see that a=1, b=-4, and c=-77


D=b%5E2-4ac Start with the discriminant formula.


D=%28-4%29%5E2-4%281%29%28-77%29 Plug in a=1, b=-4, and c=-77


D=16-4%281%29%28-77%29 Square -4 to get 16


D=16--308 Multiply 4%281%29%28-77%29 to get %284%29%28-77%29=-308


D=16%2B308 Rewrite D=16--308 as D=16%2B308


D=324 Add 16 to 308 to get 324


Since the discriminant is greater than zero, this means that there are two real solutions.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Calculate the discriminant.

Then evaluate:

Two real and unequal roots.

One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors.

A conjugate pair of complex roots of the form where is the imaginary number defined by

John