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The quadratic equation 2x^2+8x+1=0 has roots a and b. Write down the value of a+b and ab and a^2+b^2.

Since the quadratic has roots a and b, this means it can be fatored as 2(x-a)(x-b)=0. Expanding this out we get 2x^2-2(a+b)x+2ab=0 and matching the coefficients for the terms x^1 and x^0 we get a+b=-4 and ab...
JT
Answered by Joshua T. • Maths tutor
5352 Views

Why is the derivative of 2^x not x*2^(x-1)?

That technique for calculating derivatives only works for polynomial terms, that is terms of the form x^n, where n is some number. Here though our variable x is in the exponent, and so the term is not polyno...
JG
Answered by Josh G. • Maths tutor
3942 Views

Given that y = (( 4x + 1 )^3)sin(2x), find dy/dx.

This is an example of the chain rule. The chain rule is the following: if y = uv, then dy/dx = udv/dx + vdu/dx So in this case, u = ( 4x + 1)^3, v = sin(2x) du/dx = (3)(4)( 4x + 1 )^2, dv/dx = 2cos(2x) dy/dx...
DS
Answered by Danielle S. • Maths tutor
5505 Views

Find ∫ x^2(ln(4x))dx

∫x 2 ln(4x)dx Firstly , identify this question as integration by parts. Therefore set one half as value 'u' and one as value 'dv'. Here we will set u = ln(4x). Therefore: du/dx = 1/4x . (4) du = 1/x dx We th...
SF
Answered by Sally F. • Maths tutor
12036 Views

When trying to solve inequalities (e.g. 1/(x+2)>x/(x-3)) I keep getting the wrong solutions even though my algebra is correct.

*The usual mistake with inequalities is not with a students algebra, but with lack of consideration of the inequality signs. During a tutorial I would show their false method and my correct one and also sket...
TH
Answered by Timothy H. • Maths tutor
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