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I’d really appreciate some help with these problems (they should be fairly easy, I just can’t seem to remember how to do them):

(1) Find the range of k, element of R, for which x^2 + kx + k = 0 has real roots. If one of the roots of this equation is 2, find the other root.

(I’ve proved that 0 is greater than or equal to k and 4 is greater than or equal to k, using the b^2-4ac is greater than or equal to 0, but I'm stuck on the last part.)

(2) Show for any two non zero real numbers, a and b that:

(b/a^2) + (1/b) is greater than or equal to (-2/a), provided b > 0

(3) P(z) = z^3 + z, where z is an element of C. Solve the equation P(z) = 0.

(4) Show that the function f(x) = x^3 + x – 1 has a root between 0 and 1.

I know it seems like a lot to be asking for help with, but they’re just the questions I'm revising that I can’t do.

Thanks in advance for any help.

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# Homework Help: Maths questions

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