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Question
In each of the following determine whether the given values are solutions of the equation or not.
6x2 - x - 2 = 0; x = `-(1)/(2), x = (2)/(3)`
Solution
Given equation
6x2 - x - 2 = 0; x = `-(1)/(2), x = (2)/(3)`
Substitute x = `-(1)/(2)` in L.H.S.
L.H.S. = `6(-1/2)^2 - (-1/2)-2`
= `6 xx (1)/(4) + (1)/(4) - 2`
= 2 - 2
= 0
Hence, x = `-(1)/(2)` is a solution of the given equation.
Also put x = `(2)/(3)` in L.H.S.
L.H.S. = `6(2/3)^2 - (2)/(3) -2`
= `6 xx (4)/(9) - (2)/(3) - 2`
= `(8)/(3) - (2)/(3) -2`
= `(6)/(3) - 2`
= 2 - 2
= 0
Hence, x = `(2)/(3)` is a solution of the given equation.
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