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The equation x^3 - 3*x + 1 = 0 has three real roots; Show that one of the roots lies between −2 and −1

In order to prove that one real root of an equation is situated in a certain interval, we calculate the value of the function at the ends of the given interval. In the given case, f(-2) = (-2)^3 - 3*(-2) + 1...
PT
Answered by Paul T. • Maths tutor
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Complete the square and find the roots (where y=0) of: "x^2+4x-5"

completing the square: (x+2)^2-9 finding the roots: (x+2)^2=9 x+2=+/-3 at y= 0, x= -5 or 1
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Answered by Liam Q. • Maths tutor
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y=4x^3+6x+3 so find dy/dx and d^2y/dx^2

dy/dx=12x^2+6 d^2y/dx^2=24x
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Answered by Swapnil P. • Maths tutor
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How useful are these sources for our understanding of Nazi Germany from 1933 to 1939? (32 mark)

There are many aspects which contribute to our understanding of Nazi Germany within the period of 33-39. Within source A we are prevented with a satirical cartoon which grates harshly upon the regime of the ...
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Answered by Kate M. • History tutor
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The process of applying to medical school

You will formally apply to medical school in October the year before you plan to attend. Before that there are a few steps to achieve. To begin with grades are important, both at GCSE and A-level. Hard work ...
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