Question

Use the quadratic formula to solve the quadratic equation. SHOW ALL WORK. 2 −8+41 = 0

Answer 1

Answer:

Solving the equation $x^2-8x+41=0$ using quadratic formula we get $x=4+5i \ or \ x=4-5i$

Step-by-step explanation:

We need to solve the equation $x^2-8x+41=0$ using quadratic formula.

The quadratic formula is:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

where a=1, b=-8 and c=41

Putting values in formula and finding x

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-(-8)\pm\sqrt{(-8)^2-4(1)(41)}}{2(1)} \\ x=\frac{8\pm\sqrt{64-164}}{2} \\ x=\frac{8\pm\sqrt{-100}}{2} \\We \ know \ \sqrt{-1}=i\\x=\frac{8\pm10i}{2}\\x=\frac{8+10i}{2} \ or \ x=\frac{8-10i}{2}\\x=4+5i \ or \ x=4-5i$

So, Solving the equation $x^2-8x+41=0$ using quadratic formula we get $x=4+5i \ or \ x=4-5i$