Question

Use the quadratic formula to determine the roots for the following problem.

Answer 1

Step-by-step explanation

Given the expression

`2x^2-10x+17=0`

The quadratic formula is given as;

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Where

`a=2,b=-10,c=17`

We can then substitute the values of the variable into the formula to get the roots of the quadratic equation.

`\begin{gathered} x=\frac{-(-10)\pm\sqrt[]{(-10)^2-(4*2*17)}}{2*2} \\ 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}*\sqrt[]{-1}}{4} \\ x=(-10\pm6i)/(4) \\ x=(2(-5\pm3i))/(4) \\ x=(-5\pm3i)/(2) \end{gathered}`

Answer:

`x=(-5\pm3i)/(2)`