Answer: x = 1 ± i
Step-by-step explanation:
Solving the quadratic equation using the quadratic formula:
x = [tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] or [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
From the question :
a = 1
b = -2
c = 2
substituting inside the formula
X = [tex]\frac{-(-2)+\sqrt{(-2)^{2}-4(1)(2) } }{2(1)}[/tex] or
[tex]\frac{-(-2) - \sqrt{2^{2}-4(1)(2) } }{2(1)}[/tex]
x = [tex]\frac{2 + \sqrt{4-8} }{2}[/tex] or [tex]\frac{2 - \sqrt{4-8} }{2}[/tex]
x = [tex]\frac{2 + \sqrt{-4} }{2}[/tex] or [tex]\frac{2 - \sqrt{-4} }{2}[/tex]
Recall ; [tex]\sqrt{-4}[/tex] can be written as [tex]\sqrt{-1}[/tex] X [tex]\sqrt{4}[/tex], and [tex]\sqrt{-1}[/tex] = i
Substituting this
x = [tex]\frac{2+2i}{2}[/tex] or [tex]\frac{2-2i}{2}[/tex]
simplifying, we have
x = 1 + i or 1 - i
