How do you solve x^2 - 2x + 10 = 0?

2 Answers
May 14, 2018

x=1+-3i

Explanation:

"the equation is in standard form "color(white)(x)ax^2+bx+c=0

"with "a=1,b=-2" and "c=10

"there are no whole number values which allow us to"
"factor the quadratic"

"check the value of the "color(blue)"discriminant"

•color(white)(x)Delta=b^2-4ac

b^2-4ac=(-2)^2-(4xx1xx10)=4-40=-36

"since "Delta<0" then roots are complex"

"to calculate use the "color(blue)"quadratic formula"

•color(white)(x)x=(-b+-sqrt(b^2-4ac))/(2a)

rArrx=(2+-sqrt(-36))/2=(2+-6i)/2

rArrx=1+-3i

May 14, 2018

Solution: x = 1 +3 i and x = 1- 3 i

Explanation:

x^2-2 x +10=0 or x^2-2 x = -10 or

x^2-2 x +1 = 1-10 or

(x-1)^2 = -9 or (x-1) = +- sqrt (-9)

It has complex roots.

:. (x-1) = +- sqrt (9 i^2) [i^2=-1] or

(x-1) = +- 3 i or x = 1+- 3 i

Solution: x = 1 +3 i and x = 1- 3 i [Ans]