Question 390713: for the following equation, state the value of the discriminant and then describe the nature of the solutions 18x^2+10x+14=0 Found 2 solutions by jim_thompson5910, solver91311:Answer by jim_thompson5910(35256) (Show Source):
For any quadratic polynomial equation of the form:
Find the Discriminant, and evaluate the nature of the roots as follows:
No calculation quick look: If the signs on and are opposite, then guaranteed. If the signs on and are the same and both and are each greater than , then guaranteed.
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
For your problem,
, , and
Just do the arithmetic.
John
My calculator said it, I believe it, that settles it
(
