SOLUTION: for the following equation, state the value of the discriminant and then describe the nature of the solutions 18x^2+10x+14=0

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): You can put this solution on YOUR website!
From we can see that , , and

Start with the discriminant formula.

Plug in , , and

Square to get

Multiply to get

Subtract from to get

So the discriminant is

Since the discriminant is less than zero, this means that there are two complex solutions.

In other words, there are no real solutions.

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
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:

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

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