Answer:
The answer is A
[tex]x=\frac{1+i\sqrt{143} }{8}[/tex] and [tex]x=\frac{1-i\sqrt{143} }{8}[/tex]
Step-by-step explanation:
∵ 4x² - x + 9 = 0 ⇒ is quadratic equation
∴ [tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]
∴ [tex]x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
Where a is the cooficient of x² , b is the cooficient of x and c is the numerical term
∵ a = 4 , b = -1 and c = 9
∴ [tex]x=\frac{-(-1)+\sqrt{(-1)^{2}-4(4)(9) } }{2(4)} =\frac{1+\sqrt{1-144} }{8}[/tex]
[tex]=\frac{1+\sqrt{-143} }{8}=\frac{1+i\sqrt{143} }{8}[/tex]⇒ i = √(-1)
∴ [tex]x=\frac{1-i\sqrt{143} }{8}[/tex]
∴The solutions are:
x=[tex]\frac{1+i\sqrt{143} }{8}[/tex] and x=[tex]\frac{1-i\sqrt{143} }{8}[/tex]
