A) The equation has no real roots.
B) [tex]x=4\pm \sqrt{15}[/tex]
Explanation
A) 3x² + 27 = 0
Subtract 27 from both sides:
3x²+27-27 = 0-27
3x² = -27
Divide both sides by 3:
3x²/3 = -27/3
x² = -9
When we go to take the square root of both sides, we will be taking the square root of a negative number; this means there are no real roots.
B) x² - 8x + 1 = 0
I chose to complete the square. To find the value we add to both sides, take the value of b, divide by 2 and square:
(-8/2)² = (-4)² = 16
x² - 8x + 16 + 1 = 0 + 16
(x-4)² + 1 = 16
Subtract 1 from both sides:
(x-4)² + 1 - 1 = 16 - 1
(x-4)² = 15
Take the square root of both sides:
√(x-4)² = √15
x-4 = +/-√15
Add 4 to both sides:
x - 4 + 4 = 4 +/- √15
x = 4 +/- √15
