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