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

A simple way to prove this is to sub in the values that we are given. so f(x) will represent our equation x^3-3x+1 (that is f(x) = x^3-3x+1)f(-2) = -1 < 0f(-1) = 3 > 0The first thing we notice is that ...
JB
Answered by James B. • Maths tutor
10661 Views

Solve x^2 + x=12 by factorising

Start off with:x 2 +x=12Subtract 12 from both sides:x 2 +x-12=0Factorise:(x-3)(x+4)=0Solution is therefore:x=3 or x=-4
DB
Answered by Duwan B. • Maths tutor
3965 Views

If y=(a^(Sinx)) where a and k are given constants, find dy/dx in terms of a and x

Here we have to differentiate a constant raised to the power of a variable. To make it easier, let u=sinx and so our function can now be treated as y=a^u. Remembering that A = e^(LnA), a^u = e^(Ln(a^u)). Usi...
MD
Answered by Maninder D. • Maths tutor
3632 Views

Curve C has equation y=(9+11x)/(3-x-2x^2). Find the area of the curve between the interval (0, 1/2). State your answer in exact terms.

The word "area" should highlight that it is an integration question to the student. The interval asked for is (0,1/2) and so the curve should be integrated between that interval.The first task is t...
IA
Answered by Isha A. • Maths tutor
3408 Views

How can I get better at Mathematics? I am struggling with confidence and achieving low grades.

This is a really common situation so firstly, don't panic! Everyone can do well in mathematics with proper practice and you are certainly no exception. Here's my advice:Set a regular practice time, try and i...
MR
Answered by Michael R. • Maths tutor
3979 Views