I have to find the values of k

Aryan Salinas

Aryan Salinas

Answered question

2022-04-01

I have to find the values of k for which the equation:
x4(k3)x2+k=0
has: (i) four real roots and (ii) exactly 2 real roots.

Answer & Explanation

Korbin Ochoa

Korbin Ochoa

Beginner2022-04-02Added 11 answers

This has 4 real roots but those roots are pairwise equal. This means that the roots are 3,3,3,3. Your book probably means 4 distinct real roots, which this equation doesn't have.
For (ii), as you said, if (1) has a real equal positive root u, then x2=ux=±u. This also has pairwise equal roots u,u,u,u. This means that it would have 4 roots in this case.

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