Question

Use the discriminant to determine the number and type of solutions for the following equation.



24x2 – 13 = 0




A.


Zero real solutions



B.


One rational solution


C.


Two rational solutions


D.


Two irrational solutions

Answer 1

@johnweldon1993 please show me how to do this

Answer 2

It's easy to recognize that your 24x2 – 13 = 0 has the basic form\[ax^2+bx+c=0.\]What are the values of a, b and c in your 24x2 – 13 = 0

Answer 3

What does "discriminant" mean in this setting?

What is the value of \[b^2-4ac\] in this particular problem?

What does that tell you about the number and the type of solutions to 24x2 – 13 = 0?

Answer 4

it doesnt have a c

Answer 5

Sure...as mathmale has shown above...

Your equation takes the form of \(\large ax^2 + bx + c = 0\)

24x^2 - 13 = 0

Notice how 'a' is the coefficient of the x^2 ....and b is the coefficient of the x ....and 'c' is just the constant...

so it looks like your equation has

a = 24
b = 0
c = -13

The discriminant is the part of the quadratic equation that looks like

\[\large b^2 - 4ac\]

if the result is > 0 you have 2 real root
if the result is = 0 then you have 1 real root
if the result is < 0 you have 2 complex roots

so what do you get when you plug in your numbers and solve that?