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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
10538 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
3867 Views

Why does ionisation energy increase across a period?

As you go across the period, the nuclear charge (or number of protons increase) but the shielding (or the number of shells) stays the same as all of the elements are on the same period. This causes the nucle...
AP
Answered by Anjali P. • Chemistry tutor
2492 Views

Solve the quadratic equation 4x^2 - 5x -6 = 0

First factorise the equation : you need to find two value which multiply to give (4 x -6) = -24 and add to equal -5,these two numbers are -8 and 3. Then write the equation as follows:4x 2 - 8x +3x - 6 =0 We ...
KS
Answered by Katie S. • Maths tutor
8845 Views

What is the difference between these two sentences, and which one is correct: 1) La gente quiere que haya más agua. 2) La gente quieren que hay más agua.

This question tests the student's knowledge of the use of singular and plural pronouns, as well as the subjunctive. La gente (the people) is singular, so should be followed by a singular verb, as seen in sen...
DD
Answered by David D. • Spanish tutor
4407 Views