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Further Mathematics
A Level

The quadratic equation x^2-6x+14=0 has roots alpha and beta. a) Write down the value of alpha+beta and the value of alpha*beta. b) Find a quadratic equation, with integer coefficients which has roots alpha/beta and beta/alpha.

a) We know that, for a general quadratic equation that can be written as : ax2+bx+c=0, the sum of its roots (S) is equal to -b/a and the product of its roots (P...

BC
26119 Views

A useful practice: how to determine the number of solutions of a system of linear equations beforehand

We have a system of n linear equations incorporated by Ax = b, with being a n x p matrix of numeric coefficients, x being a p-dime...

FB
3538 Views

Find the determinant of a 3x3 matrix.

Will need a whiteboard so I can draw a matrix to fully explain.

SM
2741 Views

What is the modulus of 3+4i?

5

VC
2737 Views

Find the eigenvalues and corresponding eigenvectors of the following matrix: A = [[6, -3], [4, -1]]. Hence represent the matrix in diagonal form.

The first eigenvalue is 3, whose corresponding eigenvector is (1, 1), and the second eigenvalue is 2, whose corresponding eigenvector is (3, 4). In diagonal form, A = PDP^-1, where P = [[1, 3], [1, 4]] an...

MU
3060 Views

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