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For What Value of K, the Roots of the Equation X2 + 4x + K = 0 Are Real? - Mathematics

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Sum

For what value of k, the roots of the equation x2 + 4x + k = 0 are real?

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Solution

The given equation is `"x"^2 + 4"x" + "k" = 0`
For real roots, D ≥ 0
⇒ `"b"^2 – 4"ac" ≥ 0`
⇒ `4^2 – 4(1) ("k") ≥ 0`
⇒ 4 – k ≥ 0
⇒ `"k" ≤ 4`

For `"k" ≤ 4`, the given equation `"x"^2 + 4"x" + "k"` = 0 has real roots.

Concept: Nature of Roots of a Quadratic Equation
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