Find the Roots (Zeros) x^2-11x+17

$x^{2} - 11 x + 17$

Step 1

Set $x^{2} - 11 x + 17$ equal to $0$ .

$x^{2} - 11 x + 17 = 0$

Step 2

Solve for $x$ .

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = - 11$ , and $c = 17$ into the quadratic formula and solve for $x$ .

$\frac{11 \pm \sqrt{{(- 11)}^{2} - 4 \cdot (1 \cdot 17)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $- 11$ to the power of $2$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot 1 \cdot 17}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 17$ .

Multiply $- 4$ by $1$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot 17}}{2 \cdot 1}$

Multiply $- 4$ by $17$ .

$x = \frac{11 \pm \sqrt{121 - 68}}{2 \cdot 1}$

Subtract $68$ from $121$ .

$x = \frac{11 \pm \sqrt{53}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{11 \pm \sqrt{53}}{2}$

The final answer is the combination of both solutions.

$x = \frac{11 + \sqrt{53}}{2}, \frac{11 - \sqrt{53}}{2}$

$x = \frac{11 \pm \sqrt{53}}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11 \pm \sqrt{53}}{2}$

Decimal Form:

$x = 9.14005494 \dots, 1.85994505 \dots$

Step 4