) Determine whether the gives values of x is the root of given quadratic equation 6x2 - x - 2 = 0, x = 3/2
Answers
Step-by-step explanation:
Solution:
The given quadratic equation is 6x2 – x – 2 = 0
Let, x = - ½
∴ 6(- ½ )2 – (- ½ ) – 2 = 0
∴ 6 (1/4) + 1/2 – 2 = 0
∴ 3/2 + ½ - 2 = 0
∴ 4/2 - 2 = 0
∴ 2 – 2 = 0
∴ 0 = 0
Since the value of – ½ satisfies the given quadratic equation
∴ It is the root of the given quadratic equation.
Let, x = 2/3
∴ 6(2/3)2 – (2/3) – 2 = 0
∴ 6(4/9) – 2/3 – 2 = 0
∴ 8/3 – 2/3 – 2 = 0
∴ 6/3 – 2 = 0
∴ 2 – 2 = 0
∴ 0 = 0
Since the value of 2/3 satisfies the given quadratic equation
∴ It is the root of the given quadratic equation.
Let, x = 3/2 ,
∴ 6(3/2)2 – (3/2) – 2 = 0
∴ 6(9/4) – 3/2 – 2 = 0
∴ 27/2 – 3/2 – 2 = 0
∴ 24/2 – 2 = 0
∴ 12 – 2 = 0
∴ 10 ≠ 0
Since the value of 3/2 does not satisfy the given quadratic equation
∴ It is not the root of the given quadratic equation.