Question

For the following equation, state the value of the discriminate and then describe the nature of the solutions:

19x^2+4x+13=0

Answer 1

I got -972 for the value, correct? Does it have one real, two real, or two imaginary solutions?

Answer 2

Heeey, buddy. So do you know the quadratic formula? It's this whole big fancy equation that lets us solve quadratics real easily. It looks like this:
\[\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]

Now, notice the square rooted part. Everything under that is called the descriminant.

Answer 3

discriminant is \[b^2-4ac\] a=19 b=4 c=13

so discriminant is
\[4^2-4 \times19 \times 13 = -972\]

so if determinant is
two real roots > 0
1 real root = 0
no real roots or imaginary roots < 1; this is our answer

Answer 4

Ok I got the right value then, just forgot how to determine nature of solutions

Answer 5

b^2-4ac
Why is that part of the equation so important? Well, it's because of what happens when we take square roots of different kinds of numbers.
If that number is 0, then we get square root of 0 is just 0, so there's 1 solution.
If that number is positive, then we get two real answers, a positive root and a negative root.
If that number is negative, then when we try to take the square root of it, then the result is 2 complex numbers.

Answer 6

so since the discriminant is< 0, it has 2 imaginary solutions?

Answer 7

Correct, RyDaddy.

Answer 8

Thank you Smooth

Answer 9

@sugargurl swiftskier96 needs you back at the other question.

Answer 10

yeah, that graph doesn't help, gonna kill it :D

Answer 11

My pleasure =D