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In the Following Determine the Set of Values of K for Which the Given Quadratic Equation Has Real Roots: - CBSE Class 10 - Mathematics

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Question

In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]

Solution

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

\[a = 2, b = 1, c = k\]

\[D = 1 - 8k\]
The given equation will have real roots, if D≥0

\[D = 1 - 8k \geq 0\]

\[ \Rightarrow 8k \leq 1\]

\[ \Rightarrow k \leq \frac{1}{8}\]

Therefore, the value of \[k \leq \frac{1}{8}\].

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Solution In the Following Determine the Set of Values of K for Which the Given Quadratic Equation Has Real Roots: Concept: Solutions of Quadratic Equations by Factorization.
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