Question

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

Answer 1

`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`

Answer 2

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]