Solve the equation and write complex solutions in standard form. $$x ^ { 2 } - 10 x + 41 = 0$$
A) $x = - 20 - 4 i , - 20 + 4 i$
B) $x = - 4 + 5 i , - 4 - 5 i$
C) $x = 5 + 16 i , 5 - 16 i$
D) $x = 5 - 4 i , 5 + 4 i$
E) $x = - 4 + 25 i , - 4 - 25 i$

Question

Solve the equation and write complex solutions in standard form. $$x ^ { 2 } - 10 x + 41 = 0$$ 
A) $x = - 20 - 4 i , - 20 + 4 i$
B) $x = - 4 + 5 i , - 4 - 5 i$
C) $x = 5 + 16 i , 5 - 16 i$
D) $x = 5 - 4 i , 5 + 4 i$
E) $x = - 4 + 25 i , - 4 - 25 i$

Quizplus · Accepted Answer

To solve the quadratic equation $x^2 - 10x + 41 = 0$, we can use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 1$, $b = -10$, and $c = 41$. Plugging these values in, we get $x = \frac{10 \pm \sqrt{(-10)^2 - 4(1)(41)}}{2(1)} = \frac{10 \pm \sqrt{100 - 164}}{2} = \frac{10 \pm \sqrt{-64}}{2} = \frac{10 \pm 8i}{2} = 5 \pm 4i$.

Solve the Equation and Write Complex Solutions in Standard Form x2−10x+41=0x ^ { 2 } - 10 x + 41 = 0x2−10x+41=0

Solve the Equation and Write Complex Solutions in Standard Form $x ^ { 2 } - 10 x + 41 = 0$