Respuesta :
Given :
[tex]x^2\text{ - 4x + 9 = 0}[/tex]Solution
To find the roots of the equation, we can try factorizing the expression by the left.
The factors of 9 are 3,3 or 1, 9. Each of these cannot work.
So, we use the quadratic formula instead.
Given the general form of a quadratic equation:
[tex]ax^2\text{ + bx + c = 0}[/tex]The quadratic formula to find the roots of the equation is given as:
[tex]\text{x = }\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Comparing the standard form with the given equation, we have:
a = 1 , b = -4, c =9
Substituting this into the quadratic formula:
[tex]\begin{gathered} x\text{ = }\frac{-(-4)\text{ }\pm\sqrt[]{(-4)^2-\text{ 4}\times1\times9}}{2\text{ }\times\text{ 1}} \\ =\text{ }\frac{4\text{ }\pm\text{ }\sqrt[]{-20}}{2} \\ =\text{ }\frac{4\text{ }\pm\text{ }\sqrt[]{4\text{ }\times\text{ -5}}}{2} \\ =\text{ }\frac{4\text{ }\pm\text{ 2}\sqrt[]{-5}}{2} \\ =\text{ }\frac{4\text{ }\pm\text{ 2}\sqrt[]{5}i}{2} \\ \text{recall that i = }\sqrt[]{-1} \\ x\text{ = 2 }\pm\text{ i}\sqrt[]{5} \end{gathered}[/tex]Answer: Option B
