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Nature of Roots

Find the valu...

Question

Find the values of $k$ for which the following equations have real roots.
$4 x^{2} + k x + 3 = 0$

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Solution

$4 x^{2} + k x + 3 = 0$
This is in the form of $a x^{2} + b x + c = 0$
Here $a = 4, b = k, c = 3$
For the equation to have real roots ,
discriminant $\geq 0 ⟹ (k)^{2} - 4 (4) (3) \geq 0$
$⟹ (k - 4 \sqrt{3}) (k + 4 \sqrt{3}) \geq 0 ⟹ k \in (- \infty, - 4 \sqrt{3}] \cup [4 \sqrt{3}, \infty)$

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