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We need two numbers, a and b, such that a*b = 2 and a+b=3Looking at the equation it can be seen that 2 and 1 fulfill these conditions.Therefore x² +3x +2=0        = (x+2)(x+1)=0This means we ne...

Often quadratic equations of the form ax²+bx+c=0 can be easily solved by factorising. First, find pairs of numbers that multiply t...

f(c) means let x=c. Remember that c is just an unknown number.

The expression f(c)=9 means that when we put c through the function f(x)=7-4x, it gives the answer 9. Therefore we know 7-4c...

Firstly, we calculate the y-value when x=1, namely y=e. Then we need to find the gradient of this curve at x=1, which can be determined by taking the derivative of y and then valuate it at x=1. So dy/d...

There are two ways in which this we can do this,

The first is explanding the brackets to get 1+2x+x² and differentiating to get 2+2x.

The second way is using the ...