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If X = − 1 2 ,Is a Solution of the Quadratic Equation 3 X 2 + 2 K X − 3 = 0 ,Find the Value of K. - CBSE Class 10 - Mathematics

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Question

If \[x = - \frac{1}{2}\],is a solution of the quadratic equation \[3 x^2 + 2kx - 3 = 0\] ,find the value of k.

Solution

Since,  \[x = - \frac{1}{2}\],is a solution of the quadratic equation  \[3 x^2 + 2kx - 3 = 0\]

So, it satisfies the given equation.

\[\therefore 3 \left( - \frac{1}{2} \right)^2 + 2k\left( - \frac{1}{2} \right) - 3 = 0\]

\[ \Rightarrow \frac{3}{4} - k - 3 = 0\]

\[ \Rightarrow k = \frac{3}{4} - 3\]

\[ \Rightarrow k = \frac{3 - 12}{4}\]

\[ \Rightarrow k = - \frac{9}{4}\]

Thus, the value of k is \[- \frac{9}{4}\].

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Solution If X = − 1 2 ,Is a Solution of the Quadratic Equation 3 X 2 + 2 K X − 3 = 0 ,Find the Value of K. Concept: Solutions of Quadratic Equations by Factorization.
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