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Find all real values of k such that x^2 - 4kx + k = 0 has real roots.

May 19, 2020

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discrimnant of the Quadratic Equation must be positive

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

b2-4ac   is the discriminant        (-4k)^2 - 4 (1)(k) >0

16 k^2 - 4k > 0

4k (4k-1) > 0

k = 0   or 1/4

May 19, 2020