Question

The function f is defined by f(x) x2 -6x +21. What are the solutions of f(x) 0? Show your work.

Answer 1

f(x)= x^2 -6x +21

0 =x^2-6x+21

subtract 21 from each side to prepare for completing the square

-21 = x^2 -6x

completing the square (b/2)^2

(-6/2) ^ =3^2 = 9

add 9 to each side

-21 +9 = x^2 - 6x + 9

-21 +9 =(x-3) ^2

-12 = (x-3)^2

take the square root of each side

+- sqrt(-12) = x-3

add 3 to each side, take out the negative inside the square root

3 +- i sqrt(12)=x

simplify the square root  sqrt(12)= sqrt(4)sqrt(3) =2sqrt(3)

3 +- i 2sqrt (3) = x

Answer: 3+2isqrt(3)

            3-2isqrt(3)