Question

Use intergers or fractions for any numbers in the expression.

Answer 1

Quadratic Equation

A quadratic equation in the form:

$ax^2+bx+c=0$

Can be solved by using the formula:

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

We are given the function:

$f(x)=3x^2-x+3$

We can identify the variables a=3, b=-1, c=3. Applying the formula:

$x=\frac{-(-1)\pm\sqrt[]{(-1)^2-4\cdot3\cdot3}}{2\cdot3}$

Calculating:

$\begin{gathered} x=\frac{1\pm\sqrt[]{1-36}}{6} \\ x=\frac{1\pm\sqrt[]{-35}}{6} \end{gathered}$

The square root of a negative number results in an imaginary quantity. Separating the roots and using the imaginary symbol i.

$\begin{gathered} x_1=\frac{1}{6}+\frac{\sqrt[]{35}}{6}i \\ x_2=\frac{1}{6}-\frac{\sqrt[]{35}}{6}i \end{gathered}$