Couple of C3/P2 Questions - Please help

Okay, there off the C3 Specimen paper (link below)

http://www.edexcel.org.uk/VirtualContent/83441/GCE_Pure_Maths_C1_C4_Specimen_Paper_MkScheme.pdf

Q4a. I have got to the stage of: (x³+2x²-3)/ (x+3)(x-1) but cant see what they've done to get to the next step.

Q5c. i've put y=0 to get e^0 = (2x+3)^3

Hence: ³√1 = ³√(2x+3)

so: ±1 = 2x+3

Why have they taken the +ve root of 1 and not the -ve?

Thanks :smile:

Reply 1

violet

Q4a. You divide x³+2x²-3 by (x-1) by algebraic division to give (x²+3x+3)(x-1)/(x+3)(x-1)... The (x-1)'s then cancel et voila!

Reply 2

violet

Q5c. I did it this way:

y=0, so 3ln(2x+3) = 0 then divide both sides by 3 to give ln(2x+3) = 0
then 2x+3 = e^0 so 2x+3 = 1 so x = -1 therefore p = -1

Reply 3

Brigand

Why have they taken the +ve root of 1 and not the -ve?

you don't get any negative roots from cube rooting i.e the cube root of 1 is 1

Reply 4

Fermat

!Laxy!

Q5c. i've put y=0 to get e^0 = (2x+3)^3

Hence: ³√1 = ³√(2x+3)

so: ±1 = 2x+3

Why have they taken the +ve root of 1 and not the -ve?

Thanks :smile:

after you put y = 0, you got

e^0 = (2x+3)^3
or
1 = (2x+3)^3

.: (2x+3) must be +ve, since if it was -ve, then so also would be its cube!

So, express (2x+3) as the (+ve) cube root of 1.

Another reason is that you can't get a -ve (cube) root of 1!!