Determine whether the given values of 'x' are the roots of the given quadratic equation 6x2 – x – 2 = 0, x = -1/2 , x = 2/3 , x = 3/ 2

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
8/32/3 – 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
27/23/2 – 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.

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