SOLUTION: Determine the number of solutions and classify the type of solutions for each equation. Justify the answer.
x^2+3x-15=0
x^2x+4=0
x^2-8x+16=0
2x^2-3x+7=0
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Question 199156: Determine the number of solutions and classify the type of solutions for each equation. Justify the answer.
x^2+3x-15=0
x^2x+4=0
x^2-8x+16=0
2x^2-3x+7=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 
John
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