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Question
If `(2)/(3)` is a solution of the equation 7x2 + kx – 3 = 0, find the value of k.
Solution
7x2 + kx – 3 = 0, x = `(2)/(3)`
∵ x = `(2)/(3)` is its solution
∵ `7(2/3)^2 + k(2/3) - 3` = 0
⇒ `7 xx (4)/(9) + (2)/(3)k - 3` = 0
⇒ `(28)/(9) - 3 + (2)/(3)k` = 0
⇒ `(2)/(3)k = 3 - (28)/(9)`
⇒ `(2)/(3)k = (27 - 28)/(9)`
⇒ `(2)/(3)k = (-1)/(9)`
⇒ k = `(-1)/(9) xx (3)/(2)`
= `-(1)/(6)`
Hence k = `-(1)/(6)`.
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