9514 1404 393
Answer:
x = 3/2 ± i√2
Step-by-step explanation:
For quadratic ax² +bx +c = 0, the roots are given by the formula ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
When we put your equation into standard form:
4x^2 -12x +17 = 0
we see the relevant formula values are ...
a = 4, b = -12, c = 17
Then the roots are ...
[tex]x=\dfrac{-(-12)\pm\sqrt{(-12)^2-4(4)(17)}}{2(4)}=\dfrac{12\pm\sqrt{-128}}{8}\\\\x=\dfrac{3\pm2\sqrt{2}i}{2}=\boxed{\dfrac{3}{2}\pm i\sqrt{2}}[/tex]
