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tmua.me Tau Paper 2 · Q2

Paper 2AlgebraLogic & proof

For k≥0k\ge0, let M(k)M(k) be the largest number of distinct real solutions that the equation

x4+ax2+bx+1=0x^4+a x^2+b x+1=0

can have as a,ba,b range over all real numbers satisfying 20a2+9b2≤k20a^2+9b^2\le k.

What is the complete set of values of kk for which M(k)=2M(k)=2?

A(65/3,80](65/3,80]
B(65/3,90](65/3,90]
C(22,80](22,80]
D(20,80](20,80]
E[65/3,80)[65/3,80)

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