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

Question

Quizplus · Accepted Answer

To solve the equation $x^2 - 2x + 10 = 0$, we use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 1$, $b = -2$, and $c = 10$. Plugging these values in, we get $x = \frac{2 \pm \sqrt{(-2)^2 - 4(1)(10)}}{2(1)} = \frac{2 \pm \sqrt{4 - 40}}{2} = \frac{2 \pm \sqrt{-36}}{2} = \frac{2 \pm 6i}{2} = 1 \pm 3i$.

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

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