Attachment 21121

I'm on question c and I'm stuck.

Help please.

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- Mar 11th 2011, 10:20 PMeliehValues for k for distinct roots
Attachment 21121

I'm on question c and I'm stuck.

Help please. - Mar 12th 2011, 12:24 AMemakarov
The equation k = |f(x)| may have 2, 4, 6, 7 and 8 roots. Some of these numbers of roots are obtained when k is not an integer, though.

Let -m be the minimum of , i.e., is the minimum of f(x). According to my calculations, m > f(0) (0 is one of the critical points of f(x)). Therefore, when , the equation has two roots. From the inequality you can find the range of for k = 2. Then find whether gives an integer . When , the equation has 6 roots. Solving gives you the values of for k = 6, and so on.