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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 By comparing co-efficients a + 1 = 0 a - 6 = -...
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Answered by James B. • Maths tutor
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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 first c...
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Answered by Ayesha H. • Maths tutor
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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 water acts to break ...
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Answered by Lizzie F. • Geography tutor
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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 displacement. Section 2: The object is stationary . Section 3: ...
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Answered by Tomek E. • Physics tutor
6630 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 tr...
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Answered by Baptiste A. • French tutor
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