4.4 Nature of Roots: The Discriminant

Key Formulas

Solved Examples

Step 1

Condition for equal roots: Discriminant $D = 0$ .

Step 2

$a=2, b=k, c=3$ .

Step 3

$D = b^2 - 4ac = k^2 - 4(2)(3) = k^2 - 24$ .

Step 4

Set $D=0: k^2 - 24 = 0$ .

Step 5

$k^2 = 24 \implies k = \pm\sqrt{24} = \pm 2\sqrt{6}$ .

Final Answer

$k = \pm 2\sqrt{6}$

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