Re: HSC 2015 4U Marathon
Circle with centre (1,0), radius 1, excluding (0,0).
Circle with centre (1,0), radius 1, excluding (0,0).
http://imgur.com/w1DCp1x
http://imgur.com/w1DCp1x
I can't use the program (forget what it's called) that everyone uses for writing/answering questions, so:
If P(x) = x^4 - 8x^3 + 30x^2 - 56x + 49 has a non-real double zero, solve the equation P(x) = 0 over C and factorise P(x) fully over R
Here's my working, I feel as though there's a much easier solution to part i that's right under my nose, however this is the way that I did it.
Can I ask how you concluded that P(x) was that after just looking at it? I can understand that the constant of P(x) must be the square of the constant inside the brackets, but did you use any particular method for concluding that the coefficient of x (in the brackets) was -4?
I did it by equating the coefficients of the x terms. So if you just let -2Re(z)=n, then by looking at the brackets: (x^2 +nx+7)(x^2+nx+7) you know that the sum of the x terms will be 7nx+7nx which =-56x. Then 14n=-56, n=-4.Can I ask how you concluded that P(x) was that after just looking at it? I can understand that the constant of P(x) must be the square of the constant inside the brackets, but did you use any particular method for concluding that the coefficient of x (in the brackets) was -4?
Your method is good . An alternative method would be:Here's my working, I feel as though there's a much easier solution to part i that's right under my nose, however this is the way that I did it.
Next question:
If P(x) = x^6 + x^4 + x^2 + 1, show that the solutions of the equation P(x) = 0 are among the solutions of the equation x^8 - 1 = 0. Hence factorise P(x) fully over R.
https://imgur.com/AbcGhk4
a) The locus is |z - (2+2i)| = √2. This is a circle with centre (2,2), radius √2, sketched here:https://imgur.com/AbcGhk4
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z satisfies the equation |z - 2 - 2i| = √2.
a) Sketch the locus of the point P representing z on an Argand diagram.
b) Find the maximum and minimum values of |z| and the values of z for which these extremes are attained.
c) Find the range of possible values of arg z.
Denote the equation by . Let be a root of , where and (so ). We show that r must be greater than ½.NEXT QUESTION
Prove that all the roots of the equation
I have got as far as saying that tanx - sinx + cosx = 1, but don't really know where to go from there
If the expression is real, find the set of all possible values for .
I have got as far as saying that tanx - sinx + cosx = 1, but don't really know where to go from there
LaTeX Bruhjust wondering but what method did you use to input mathematics online like that Sy123?
This forum has built-in LaTeX generatorjust wondering but what method did you use to input mathematics online like that Sy123?