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Question
In each of the following, determine whether the given numbers are roots of the given equations or not; 6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
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Solution
6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
If x = `(-1)/(2)`, then
= `6(-1/2)^2 - (-1/2) - 2`
= `6 xx (1)/(4) + (1)/(2) - 2`
= `(3)/(2) + (1)/(2) - 2`
= `(4)/(2) - 2` = 0
∴ x = `(-1)/(2)` is its root
If x = `(2)/(3)`, then
= `6 xx (4)/(9) - (2)/(3) - 2`
= `(8)/(3) - (2)/(3) - 2`
= `(6)/(3) - 2` = 0
∴ x = `(2)/(3)` is also its root.
Hence `(-1)/(2), (2)/(3)` are both its root.
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