Explanation
Given the expression
[tex]2x^2-10x+17=0[/tex]
The quadratic formula is given as;
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
Where
[tex]a=2,b=-10,c=17[/tex]
We can then substitute the values of the variable into the formula to get the roots of the quadratic equation.
[tex]\begin{gathered} x=\frac{-(-10)\pm\sqrt[]{(-10)^2-(4\times2\times17)}}{2\times2} \\ x=\frac{10\pm\sqrt[]{100-136}}{4} \\ x=\frac{-10\pm\sqrt[]{-36}}{4} \\ \text{Since i =}\sqrt[]{-1} \\ x=\frac{-10\pm\sqrt[]{36}\times\sqrt[]{-1}}{4} \\ x=\frac{-10\pm6i}{4} \\ x=\frac{2(-5\pm3i)}{4} \\ x=\frac{-5\pm3i}{2} \end{gathered}[/tex]
Answer:
[tex]x=\frac{-5\pm3i}{2}[/tex]
