SOLUTION: Determine what type of solutions the quadratic equation x²+ 3x – 7 = 0 offers.
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Question 326247: Determine what type of solutions the quadratic equation x²+ 3x – 7 = 0 offers.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
For any quadratic polynomial equation of the form:
Find the Discriminant, 
and evaluate the nature of the roots as follows:
Two real and unequal roots. If 
is a perfect square, the quadratic factors over 
.
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 
But here is a shortcut. Whenever the signs on 
and 
are opposite as in this problem, 
is guaranteed.
John
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