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For x!=0, multiply the equation by x to get x^4+5x^2+1=0. Then substitute t=x^2 where t>=0. So the equation has a form t^2+5t+1. Then find the discriminant and two roots. One of the roots t2<0 doesn...

Get a line a form y=-ax/b-c/b, then substitute into a cirle equation (x-p)^2 +(y-s)^2=r^2. Get a quadratic and find whether a discriminant is equal to zero. If it is then the line is tangent to a circle. ...

Because by looking at the second derivative of a function you are essentially looking at the rate of change of the rate of change. This carries useful information about a function's behaviour and in some ...

A 2x2 square matrix is of the format (a b;c d). First you must check whether the matrix is invertible at all: if ad - bc is 0, the matrix is not invertible. The inverse matrix is (1/(ad-bc))*(d -...

The product rule is used to differentiate a function when it is in the form y= u(x)v(x). To use the rule you differentiate u(x) and multiply that by v(x), and then add that to the differential of v(x)...