Answer:
[tex]c < \frac{9}{8}[/tex]
For all c less than [tex]\frac{9}{8}[/tex] ,the given quadratic equation has no real number solutions.
Step-by-step explanation:
Given
Quadratic Equation
[tex]-2x^{2} + 3x + c = 0[/tex]
On comparing with general form of Quadratic Equation
[tex]Ax^{2}+ Bx + C = 0[/tex]
we have,
[tex]A=-2\\B=3\\C=c\\[/tex]
For no real number solution we must have
[tex]Discriminant, B^{2}- 4AC < 0\\(3)^{2} - 4\times -2\times c < 0\\9-8c < 0\\-8c < -9\\c < \frac{9}{8}[/tex]
So, For all c less than [tex]\frac{9}{8}[/tex] ,the given quadratic equation has no real number solutions.
