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given the quadratic equation x²-x-6=0 , find the roots in three methods
A. Factoring
B. Completing the square
C. Quadratic Formula​

Sagot :

Nyle07idn

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

  • Add 6 to 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. :)

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