we use quadratic formula for that one
remember that √-1=i
so
for
ax^2+bx+c=0
[tex]x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}[/tex]
so
given
4x^2-5x+2=0
a=4
b=-5
c=2
[tex]x=\frac{-(-5)+/-\sqrt{(-5)^2-4(4)(2)}}{2(4)}[/tex]
[tex]x=\frac{5+/-\sqrt{25-32}}{8}[/tex]
[tex]x=\frac{5+/-\sqrt{-7}}{8}[/tex]
[tex]x=\frac{5+/-i\sqrt{7}}{8}[/tex]
so in complex form (a+bi)
[tex]x=\frac{5}{8}+\frac{i\sqrt{7}}{8}, \frac{5}{8}-\frac{i\sqrt{7}}{8}[/tex]
