Search over 10,000 free study notes

x=5 is a solution, so (x-5) is a factor of f(x). So, to find the other solutions, factorise f(x): f(x)=(x-5)(ax^2+bx+c). We know it will be of this form because f(x) is cubic. To find the values of a, b a...

The first step is to find the complementary function, yc, which is done by setting up a quadratic based upon the differential equation of the form m^2 + m -2 = 0 (i.e m^2 = d2y/dx2, m = dy/dx, and y is a ...

Finding the matrix of a matrix can be done in 5 steps. Step 1 involves finding the determinant of the matrix, and putting this value aside for later. Step 2 finds the cofactors of each element. The cofact...

The first thought when trying to solve such a problem is that you might be able to write this sum as a geometric progression. Luckily, it is the case here as well, as we can observe that S is the derivati...

To show something is a subgroup we need to show that it satisfies the group axioms. Therefore we need to show that if g and h are in Z(G) then gh is in Z(G), g^-1 is in Z(G), the identity e is in Z(G). As...