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Show that the cubic function f(x) = x^3 - 7x - 6 has a root x = -1 and hence factorise it fully.

f(-1) = (-1)^3 - (-1)*7 - 6 = -1 + 7 - 6 = 0

Hence f(x) = (x+1)(x^2 + ax - 6)

Expand this out

f(x) = x^3 + ax^2 - 6x + x^2 + ax - 6 

      = x^3 + (a+1)x^2 + (a-6)x -6

B...

JB
Answered by James B. Maths tutor
4201 Views

What is Mathematical Induction?

Mathematical induction is a type of direct proof, where you can prove sequences or series. A good example of this is that we can prove 1 + 3 + 5 + .... + (2n-1) = n^2. There are 4 steps: 1. Prove the firs...

AH
Answered by Ayesha H. Maths tutor
3826 Views

Describe the main forms of river erosion.

Erosion is the wearing away of the bank of the river as well as the bedload it transports. There are four main forms of river erosion. Firstly, Hydraulic action is where the force of the ...

LF
Answered by Lizzie F. Geography tutor
2963 Views

Describe the motion of a moving object with a given Displacement-Time graph. For each section on the graph, indicate the direction of motion and identify if the object is accelerating or not. What would the object's Velocity-Time graph look like?

Section 1: The object is moving away from its origin with a constant speed. There is no acceleration as demonstrated by the linear increase in displaceme...

TE
Answered by Tomek E. Physics tutor
6142 Views

Reformulez chacune des phrases ci-dessous, en commençant votre réponse avec les mots donnés entre parenthèses: La technologie n’est pas difficile à installer. (Il … )

The goal of this exercise is to rewrite the sentence by starting it with the word between parenthesis. To achieve that properly we will break down this sentence in several pieces. But first of all we will...

BA
Answered by Baptiste A. French tutor
3431 Views

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