Find all solutions of the equation $$x ^ { 2 } - 2 x + 10 = 0$$ and express them in the form a + bi.
A) $x = 3 + 2 i , x = 3 - 2 i$
B) $x = 1 + 3 i , x = 1 - 3 i$
C) $x = 1 , x = - 1$
D) $x = 4 + 12 i , x = 4 - 12 i$
E) no solutions

Question

Find all solutions of the equation $$x ^ { 2 } - 2 x + 10 = 0$$ and express them in the form a + bi. 
A) $x = 3 + 2 i , x = 3 - 2 i$
B) $x = 1 + 3 i , x = 1 - 3 i$
C) $x = 1 , x = - 1$
D) $x = 4 + 12 i , x = 4 - 12 i$
E) no solutions

Quizplus · Accepted Answer

Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a = 1$, $b = -2$, and $c = 10$, we find the discriminant $b^2 - 4ac = (-2)^2 - 4(1)(10) = 4 - 40 = -36$. Since the discriminant is negative, the solutions are complex: $x = \frac{2 \pm \sqrt{-36}}{2} = 1 \pm 3i$.

Find All Solutions of the Equation x2−2x+10=0x ^ { 2 } - 2 x + 10 = 0x2−2x+10=0

Find All Solutions of the Equation $x ^ { 2 } - 2 x + 10 = 0$