A. FACTORING:
x² - x - 6 = 0
(x - 3) (x + 2) = 0
Solve for the roots:
x - 3 = 0
x = 3
x + 2 = 0
x = -2
B. COMPLETING THE SQUARE
x² - x - 6 = 0
- In order to complete the square, the equation must be in the form ax² + bx = c.
- Add 6 to both sides of the equation
x² - x = 6
- Divide -1, the coefficient of x term, by 2 to get -1/2. Then add the square of -1/2 to both sides of the equation. This step makes the left side of the equation a perfect square trinomial.
x² - x + (-1/2)^2 = 6 + (-1/2)^2
x² - x + (-1/2)^2 = 6 + (-1/2)^2
x² - x + 1/4 = 6 + 1/4
x² - x + 1/4 = 25/4
- Factor x² - x + 1/4, using a square of the binomial rule.
(x - 1/2)^2 = 25/4
- Take the square root of both sides of the equation
√(x - 1/2)^2 = √25/4
(x - 1/2) = ± 5/2
Solve for the roots:
x - 1/2 = 5/2
x = 1/2 + 5/2
x = 6/2
x = 3
x -1/2 = - 5/2
x = 1/2 - 5/2
x = -4/2
x = -2
C. QUADRATIC FORMULA
x² - x - 6 = 0
- Use the formula x = -b ± √b² - 4ac / 2a.
1. Identify the values of a, b & c
a = 1
b = -1
c = -6
2. Substitute the values to the formula x = -b ± √b² - 4ac / 2a.
x = -(-1) ± √1 - 4(1)(-6) / 2
x = -(-1) ± √1 + 24 / 2
x = -(-1) ± √25 / 2
- Take the square root of 25.
x = -(-1) ± 5 / 2
x = 1 ± 5 / 2
Solve for the roots:
x = 1 + 5/ 2
x = 6/2
x = 3
x = 1 - 5/ 2
x = -4/2
x = -2
- Based on the three methods of finding the roots of x² - x - 6 = 0, we can conclude that the roots are fixed or can't be changed. You will get the same result, despite different ways of methods to solve it.
- I hope this can help you a lot. :)
#CarryOnLearning
