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Mathematics

If x = −12\dfrac{-1}{2} is a solution of the quadratic equation 3x2 + 2kx - 3 = 0, then the value of k is:

  1. −34-\dfrac{3}{4}

  2. −54-\dfrac{5}{4}

  3. −94-\dfrac{9}{4}

  4. −45-\dfrac{4}{5}

Quadratic Equations

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Answer

Given,

x = −12\dfrac{-1}{2}

Equation : 3x2 + 2kx - 3 = 0

Substituting value of x in equation:

⇒3x2+2kx−3=0⇒3(−12)2+2k(−12)−3=0⇒3(14)−k−3=0⇒(34)−k=3⇒k=34−3⇒k=3−124⇒k=−94.\Rightarrow 3x^2 + 2kx - 3 = 0 \\[1em] \Rightarrow 3\Big(\dfrac{-1}{2}\Big)^2 + 2k\Big(\dfrac{-1}{2}\Big) - 3 = 0 \\[1em] \Rightarrow 3\Big(\dfrac{1}{4}\Big) - k - 3 = 0 \\[1em] \Rightarrow \Big(\dfrac{3}{4}\Big) - k = 3 \\[1em] \Rightarrow k = \dfrac{3}{4} - 3 \\[1em] \Rightarrow k = \dfrac{3 - 12}{4} \\[1em] \Rightarrow k = -\dfrac{9}{4}.

Hence, option 3 is the correct option.

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