The Student Room Group

What does this question mean?

96.PNG
What does part one of iv) mean lol - I am not really sure what I am supposed to do
Jesus focking christ i chose a level maths R.I.P me
oh you equate the equation of the curve equals the equation of the straight line . Yc=Yl, then you bring all the variables to the left side . Then you put the values of x co ordinates of the intersections that you found graphically in this equation that u just derived and show that for all the x co ordinates of the intersection points it equals Zero. If you require further help do let me know
Original post by Kalabamboo

What does part one of iv) mean lol - I am not really sure what I am supposed to do


Intersections between y=5x+10y=5x+10 and y=2x3+11x2βˆ’xβˆ’30y=2x^3+11x^2-x-30 are given by the equation 5x+10=2x3+11x2βˆ’xβˆ’305x+10 = 2x^3+11x^2-x-30 which can be rearranged into 2x3+11x2βˆ’6xβˆ’40=02x^3+11x^2-6x-40=0.

You know one of these intersections has component x=βˆ’2x=-2 therefore (x+2)(x+2) is a factor of 2x3+11x2βˆ’6xβˆ’40=02x^3+11x^2-6x-40=0. There are two more factors (xβˆ’a)(x-a) and (xβˆ’b)(x-b) from the other two solutions x=ax=a and x=bx=b.

It should be clear that 2x3+11x2βˆ’6xβˆ’40=2(x+2)(xβˆ’a)(xβˆ’b)2x^3+11x^2-6x-40 = 2(x+2)(x-a)(x-b), hence 2x3+11x2βˆ’6xβˆ’40x+2=2(xβˆ’a)(xβˆ’b)\dfrac{2x^3+11x^2-6x-40}{x+2} = 2(x-a)(x-b).

The question wants you to show that the other two roots satisfy 2(xβˆ’a)(xβˆ’b)=2x2+7xβˆ’20=02(x-a)(x-b)=2x^2+7x-20=0. So, perform long division on the LHS to determine this.
Reply 4
Original post by RDKGames
Intersections between y=5x+10y=5x+10 and y=2x3+11x2βˆ’xβˆ’30y=2x^3+11x^2-x-30 are given by the equation 5x+10=2x3+11x2βˆ’xβˆ’305x+10 = 2x^3+11x^2-x-30 which can be rearranged into 2x3+11x2βˆ’6xβˆ’40=02x^3+11x^2-6x-40=0.

You know one of these intersections has component x=βˆ’2x=-2 therefore (x+2)(x+2) is a factor of 2x3+11x2βˆ’6xβˆ’40=02x^3+11x^2-6x-40=0. There are two more factors (xβˆ’a)(x-a) and (xβˆ’b)(x-b) from the other two solutions x=ax=a and x=bx=b.

It should be clear that 2x3+11x2βˆ’6xβˆ’40=2(x+2)(xβˆ’a)(xβˆ’b)2x^3+11x^2-6x-40 = 2(x+2)(x-a)(x-b), hence 2x3+11x2βˆ’6xβˆ’40x+2=2(xβˆ’a)(xβˆ’b)\dfrac{2x^3+11x^2-6x-40}{x+2} = 2(x-a)(x-b).

The question wants you to show that the other two roots satisfy 2(xβˆ’a)(xβˆ’b)=2x2+7xβˆ’20=02(x-a)(x-b)=2x^2+7x-20=0. So, perform long division on the LHS to determine this.

Thanks a lot for your reply once again! But why is there a 2 in front of (x+2) for your 3rd bullet point?
Original post by Kalabamboo
Thanks a lot for your reply once again! But why is there a 2 in front of (x+2) for your 3rd bullet point?


Without it, you would expand the brackets and end up with x3x^3 instead of 2x32x^3 like the LHS requires. So you need it.
Reply 6
Original post by RDKGames
Without it, you would expand the brackets and end up with x3x^3 instead of 2x32x^3 like the LHS requires. So you need it.


Ah thanks a lot! And also shouldn't it be 2(x+a)(x+b) = 2x^2 +7x-20?

Btw thank you for helping me with so many of my questions today:smile:
(edited 5 years ago)
Original post by Kalabamboo
Ah thanks a lot! And also shouldn't it be 2(x+a)(x+b) = 2x^2 +7x-20?

Btw thank you for helping me with so many of my questions today:smile:


Not necessarily. You can have that if you want but then the roots are x=-a and x=-b.
Reply 8
Original post by RDKGames
Not necessarily. You can have that if you want but then the roots are x=-a and x=-b.

Oh wait actually isn't it 2(x+a)(x-b) cause the "other" roots are x=-5.3 and x=1.8 ?
Why do you say you can have that - is that also correct?
Original post by Kalabamboo
Oh wait actually isn't it 2(x+a)(x-b) cause the "other" roots are x=-5.3 and x=1.8 ?
Why do you say you can have that - is that also correct?


Sure. As long as either bracket is =0 whenever x=-5.3 or x=1.8. So 2(x+5.3)(x-1.8)

Anyway it’s late and this is my last post for today. Good luck!
(edited 5 years ago)
Original post by RDKGames
Sure. As long as either bracket is =0 whenever x=-5.3 or x=1.8. So 2(x+5.3)(x-1.8)

Anyway it’s late and this is my last post for today. Good luck!

Thanks a lot!! goodnight!

Quick Reply

Latest