1. Solve each equation, if possible. Write irrational numbers in the simplest radical form. Describe the strategy you used to get your solution and tell me why you chose it.a. 3x^2 + 27 = 0b. x^2 - 8x + 1 = 0
Accepted Solution
A:
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