SOLUTION: Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer. a) x2 + 3x

SOLUTION: Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer. a) x2 + 3x - 15 = 0 b) x2 + x + 4 = 0 c) x2

Question 198819: Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer.
a) x2 + 3x - 15 = 0
b) x2 + x + 4 = 0
c) x2 � 4x - 7 = 0
d) x2 � 8x + 16 = 0
e) 2x2 - 3x + 7 = 0
f) x2 � 4x - 77 = 0
g) 3x2 - 7x + 6 = 0
h) 4x2 + 16x + 16 = 0
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Each of these problems is in the form:

For each of them, calculate the discriminant (

Then evaluate the character of the roots based on the value of

according to the following criteria (which presume rational coefficients on your quadratic):

Two real and unequal roots. If

is a perfect square, then both roots are rational. Otherwise the two roots are a conjugate pair of irrational roots of the form

where

is rational and

is irrational.

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

By the way, if you thought that you could just drop your entire homework assignment in here and get someone to do it for you, let me disabuse you of that notion right now.

John

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