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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
4481 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
4081 Views

You have a cubiod of dimension 2.2m by 1.8m by 2.0m, you have a pole of length 3m. Will the pole fit into the cuboid?

The longest straight line within the cuboid is the diagonal from a corner to the corner diagonally from it (show diagram), call this D. So to find out whether the pole will fit, find this length, if it is...

GJ
Answered by Grace J. Maths tutor
4456 Views

You are given that f(x) = cx + d and that f(0) = -6 and f(2) = 10. Find the values of c and d.

f(x) = cx + d f(0) = c0 + d = d = -6 => d = -6 f(2) = c2 + d = c2 + -6 = 10 => c2 - 6 = 10 => c = (10 + 6) / 2 => c = 8

GJ
Answered by Grace J. Maths tutor
6927 Views

Find the value of x in (4^5⋅x+32^2)⋅2^5=2^16⋅x

Find the value of x in (45x+322)⋅25=216x

First we transform everything into powers of 2 as all the numbers involved in...

LC
Answered by Luis C. Maths tutor
7488 Views

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