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The cubic equation 27(z^3) + k(z^2) + 4 = 0 has roots α, β and γ. In the case where β=γ, find the roots of the equation and determine the value of k

This question was worth 8 marks in a 2015 FP2 paper. The first part of this question is tricky, but once we have found the roots it will be easy to plug them in to get the value of k: When we have an equatio...
RG
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The set of midpoints of the parallel chords of an ellipse with gradient, constant 'm', lie on a straight line: find its equation; equation of ellipse: x^2 + 4y^2 = 4

// Allow me to make the question more explicit: we have a set of lines of equal gradients ‘m’. We need to find a line through which the midpoints of the intersections of these lines with the ellipse; an elli...
DP
5752 Views

How and when do I use the subjunctive?

The subjunctive in French is used when talking about theoretical situations, and also with certain phrases using 'que' - this can be tricky, because the 'que' phrases must be learnt. The subjunctive is also ...
JO
Answered by Jennifer O. • French tutor
5420 Views

Differentiate a^x with respect to x

y=a^x take natural logs (also written as ln or log base e) of both sides lny=lna^x by logarithms rules lna^x=xlna lny=xlna Now differentiate implicitly 1/y = (dx/dy)lna Note here lna is just a constant, then...
JM
Answered by James M. • Maths tutor
43233 Views

Resolving the forces for an object suspended on two strings.

Imagine a following situation: a stationary (not moving) object with a mass of 5 kg is suspended in the air by two strings. The angles between strings and the vertical directions are 15 and 55 degrees. What ...
FW
Answered by Filip W. • Physics tutor
20213 Views