Answer:
zero real solutions
Step-by-step explanation:
You want the number of real roots of 3x² -5x +4 = 0 and determined by using the discriminant.
Discriminant
The discriminant of a quadratic equation ax²+bx+c=0 is ...
d = b² -4ac
When d < 0, both roots are complex. When d = 0, there is one (repeated) real root. The number of real solutions is 2 when d > 0.
Application
For this equation, a=3, b=-5, c=4, so the discriminant is ...
d = b² -4ac = (-5)² -4(3)(4) = 25 -48 = -23
This means both roots are complex. There are no real solutions.
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Additional comment
As confirmation, we can look at the graph. It does not cross the x-axis, so there are no (real) values of x that make the value of the quadratic be zero.
