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Given that α= 1+3i is a root of the equation z^3 - pz^2 + 18z - q = 0 where p and q are real, find the other roots, then p and q.

All coefficients of z are real, therefore one root must be the complex conjugate so β = 1-3i.It is known that Σαβ = 18 (the coefficient of z), so we can get an equation in the third root, γ, as follows: Σαβ ...
ZG
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How do you integrate sin^2(3x)cos^3(3x) dx?

Use the identity sin^2(y) + cos^2(y) = 1 to get the expression sin^2(3x) (1-sin^2(3x)) cos(3x) dx.Use the substitution u= sin(3x) by dividing the expression by the derivative, u’= 3cos(3x).The expression the...
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Answered by Zachary G. • Maths tutor
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How should I structure an answer to a Philosophy essay?

The first thing you should do is Plan. You need to think about what points you will make, the responses and counter-responses you will discuss and how you will conclude.This is the best way to make sure your...
ZG
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Write a short commentary on a passage from Margaret Atwood's "The Handmaid's Tale."

In this extract, we see Offred bathing and considering her existence. This scene can be seen as an extended metaphor for the conflict that Offred is experiencing between memories of a former life and her new...
RI
Answered by Rhiannon I. • English tutor
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Express the equation x^2+6x-12 in the form (x+p)^2+q

To work out the value of p, half the x coefficient EG:6/2=3. Then work out the square EG: (x+3)^2=x^2+6x+9. To work out the value for q, place the constant of the original equation equal to the constant of t...
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Answered by Isabel S. • Maths tutor
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