Answer:
see the explanation
Step-by-step explanation:
<u><em>The correct question is</em></u>
Use the discriminant to determine how many solutions are possible for the following equation (show work).
5x^2-3x+4=0
we know that
The discriminant for a quadratic equation of the form
is equal to
![D=b^2-4ac](https://tex.z-dn.net/?f=D%3Db%5E2-4ac)
If D=0 then the equation has only one real solution
If D>0 then the equation has two real solutions
If D<0 then the equation has no real solutions (two complex solutions)
in this problem we have
so
![a=5\\b=-3\\c=4](https://tex.z-dn.net/?f=a%3D5%5C%5Cb%3D-3%5C%5Cc%3D4)
substitute
![D=-3^2-4(5)(4)](https://tex.z-dn.net/?f=D%3D-3%5E2-4%285%29%284%29)
![D=-71](https://tex.z-dn.net/?f=D%3D-71)
so
The equation has no real solutions, The equation has two complex solutions
therefore
I know there are___No____
real solutions to the equation in problem 4 because ___the discriminant is negative___