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प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]
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उत्तर
The given quadric equation is \[2 x^2 + x + k = 0\],and roots are real.
Then find the value of k.
Here,
\[a = 2, b = 1, c = k\]
As we know that `D = b^2 - 4ac`
Putting the value of
\[a = 2, b = 1, c = k\]
\[D = 1 - 8k \geq 0\]
\[ \Rightarrow 8k \leq 1\]
\[ \Rightarrow k \leq \frac{1}{8}\]
Therefore, the value of \[k \leq \frac{1}{8}\].
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