Use the Quadratic Formula to solve the quadratic below $\newline$ $x^{2}-5 x+9=0$ $\newline$ Desmos Scientific Calculator $\newline$ Show Your Work

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Algebra 2

Quadratic equation with complex roots

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Q. Use the Quadratic Formula to solve the quadratic below

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x^{2}-5 x+9=0

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Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic equation $x^2 - 5x + 9 = 0$ . The standard form of a quadratic equation is $ax^2 + bx + c = 0$ . Comparing this with our equation, we find that $a = 1$ , $b = -5$ , and $c = 9$ .
Write Quadratic Formula: Write down the Quadratic Formula. $\newline$ The Quadratic Formula is $(-b \pm \sqrt{b^2 - 4ac}) / (2a)$ . We will use this formula to find the roots of the equation.
Substitute values: Substitute the values of $a$ , $b$ , and $c$ into the Quadratic Formula. $\newline$ Substitute $a = 1$ , $b = -5$ , and $c = 9$ into the formula to get the roots of the equation. $\newline$ $\frac{-(-5) \pm \sqrt{(-5)^2 - 4 \cdot 1 \cdot 9}}{2 \cdot 1}$
Simplify terms: Simplify the terms inside the square root and outside. $\newline$ Calculate the discriminant (the expression inside the square root) and simplify the constants outside the square root. $\newline$ $\frac{5 \pm \sqrt{25 - 36}}{2}$
Simplify square root: Simplify the expression under the square root. Since $25 - 36 = -11$ , we have a negative number under the square root, which indicates that the roots will be complex numbers. $(5 \pm \sqrt{-11}) / 2$
Express in terms of i: Express the square root of the negative number in terms of i, where i is the imaginary unit. $\newline$ $\sqrt{-11}$ can be written as $\sqrt{11} \cdot i$ , since i is defined as $\sqrt{-1}$ . $\newline$ $(5 \pm \sqrt{11} \cdot i) / 2$
Divide by $2$ : Simplify the expression by dividing both terms by $2$ . $\frac{5}{2}$ $\pm$ $\frac{\sqrt{11}}{2}$ * $i$
Write roots in $a+bi$ form: Write the roots in the simplest $a+bi$ form. Express the roots as two separate terms, one with the plus sign and one with the minus sign. $\frac{5}{2} + \left(\frac{\sqrt{11}}{2}\right) * i$ & $\frac{5}{2} - \left(\frac{\sqrt{11}}{2}\right) * i$