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If 12-\dfrac{1}{2} is the solution of the equation 3x2 + 2kx - 3 = 0, find the value of k.

Quadratic Equations

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Answer

Since, 12-\dfrac{1}{2} is a solution of the equation 3x2 + 2kx - 3 = 0, x = 12-\dfrac{1}{2} satisfies the given equation.

Substituting x = 12-\dfrac{1}{2} and solving for k we get:

3(12)2+2k(12)3=03×14k3=0k=334k=343k=3124k=943\Big(-\dfrac{1}{2}\Big)^2 + 2k \Big(-\dfrac{1}{2}\Big) -3 = 0 \\[1em] \Rightarrow 3 \times \dfrac{1}{4} - k - 3 = 0 \\[1em] \Rightarrow -k = 3 - \dfrac{3}{4} \\[1em] \Rightarrow k = \dfrac{3}{4} - 3 \\[1em] \Rightarrow k = \dfrac{3 - 12}{4} \\[1em] \Rightarrow k = -\dfrac{9}{4}

Hence, the value of k is 94-\dfrac{9}{4}

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