Answer:
The quadratic equation [tex]2\, x^{2} - 3\, x + 8 = 0[/tex] has no real solution.
Step-by-step explanation:
Rewrite the quadratic equation [tex]2\, x^{2} - 3\, x + 8 = 0[/tex] in the standard form [tex]a\, x^{2} + b\, x + c = 0[/tex]:
[tex]2\, x^{2} + (-3)\, x + 8 = 0[/tex], for which:
- [tex]a = 2[/tex].
- [tex]b = (-3)[/tex].
- [tex]c = 8[/tex].
The quadratic discriminant of [tex]a\, x^{2} + b\, x + c = 0[/tex] is [tex](b^{2} - 4\, a\, c)[/tex]. The quadratic discriminant of [tex]2\, x^{2} + (-3)\, x + 8 = 0[/tex] would be:
[tex]\begin{aligned}& b^{2} - 4\, a\, c \\ =\; & (-3)^{2} - 4 \times 2 \times 8 \\ =\; & (-55)\end{aligned}[/tex].
Since the quadratic discriminant of this equation is negative, this quadratic equation has no real solution.
