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A cubic polynomial has the form p(z)=z^3+bz^2+cz+d, z is Complex and b, c, d are Real. Given that a solution of p(z)=0 is z1=3-2i and that p(-2)=0, find the values of b, c and d.

I will explain this choice of question and demonstrate my approach of showing the most forward way to solve this in the interview.

Answered by • Maths tutor

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Jill and four friends go camping together for 5 days. The friends share the cost of the trip equally. These costs are: £120 for fuel, £58 for food, £100 for equipment and £207 for activities. How much does Jill have to pay for her share of the costs?

The first thing we need to realise that the cost of the trip is going to be split between 5 people (Jill + 4 friends). As they are all sharing the cost of the trip equally, we need to find the total cost ...

Answered by Lauren D. • Maths tutor

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how do I solve the equation x^2 + 7x + 11 = 0, to 3dp?

This is a quadratic equation and there are three ways to solve one. This question specifies that the answer should be left to three decimal places. This tells you that you can not factorise, as your...

Answered by Jamie D. • Maths tutor

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Let f (x) = 5x and g(x) = x2 + 1 , for x ∈  . (a) Find f-1(x) . (b) Find ( f ° g) (7) .

a,y=5xfinding the inverse: x=5y - dividing by 5 (1/5)x=y f^-1(x)=(1/5)x
b,5x(7²+1)=250

Answered by • Maths tutor

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Differentiate f = ln(x^2 + 1) / (x ^ 2 + 1).

We'll apply the quotient rule using "u = ln(x²+ 1)" and "v = x² + 1". First we'll need to calculate u' and v'.Using normal differentiation rules, we can see &quo...

Answered by William P. • Maths tutor

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