An algebra problem by Tanishq Varshney

Algebra Level 5

Given that x4+(12k)x2+k21=0x^4+(1-2k)x^2+k^2-1=0, where kk is real, has no real roots when x2x^2 is imaginary or x2<0x^2<0 and has real roots when x20x^2\ge 0.

Find the range of kk, when the equation has four distinct real roots.

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