Answer:
complex numbers
x = (3 - √23i) / 4 , x = (3 + √23i) / 4
Explanation:
Given in the question that polynomial equation is
-2x² + 3x - 4 = 0
It is a quadratic equation which can be solve by using quadratic formula
x = −b ± √(b² − 4ac) / 2a
where a = -2
b = 3
c = -4
x = -(3) ± √(-3)² - 4(-2)(-4) / 2(-2)
x = -3 ± √9 - 4(8) /2(-2)
x = -3 ± √9 -32 / -4
x = (-3 + √9 -32) / -4 , x = (-3 - √9 -32) / -4
x = (-3 + √-23) / -4 , x = (-3 - √-23) / -4
x = (-3 + √23i) / -4 , x = (-3 - √23i) / -4
x = (3 - √23i) / 4 , x = (3 + √23i) / 4