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Maths Help

. One of the roots of x3 – 2x(sqaured) – px + 12 = 0 is 4.
Calculate p and hence find the other roots of this polynomial.
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Original post by Misshussain23
. One of the roots of x3 – 2x(sqaured) – px + 12 = 0 is 4.
Calculate p and hence find the other roots of this polynomial.


Do you remember the factor theorem?
If 4 is a root of the equation then f(4) = 0
Evaluate for x=4 and solve for p

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(edited 8 years ago)
Original post by gdunne42
Do you remember the factor theorem?
If 4 is a root of the equation then f(4) = 0
Evaluate for x=4 and solve for p

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Yeah thanks i got that part but not sure how to find the other roots because every factor 12 i put in the l shape eqn is not giving the ansewer of 0
Original post by Misshussain23
Yeah thanks i got that part but not sure how to find the other roots because every factor 12 i put in the l shape eqn is not giving the ansewer of 0


If x=4 is a root, then (x-4) is a factor, so do the polynomial/long division and you're left with a quadratic to solve.

Alternatively: Since 4 is one root, then you're only interested in factors of 12/4=3 for the other two. There are only 4 to choose from.
(edited 8 years ago)
ImageUploadedByStudent Room1449574133.045758.jpg

Could I please have help on how to answer this question. I thought it was differentiation and the equation of a tangent where you find the ran for the straight line but I'm not sure


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Original post by Misshussain23
ImageUploadedByStudent Room1449574133.045758.jpg

Could I please have help on how to answer this question. I thought it was differentiation and the equation of a tangent where you find the ran for the straight line but I'm not sure


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Yes. You need the tangent to make an angle of 45 with the positive x-axis.

And since the tan of that angle is equal to the derivative, you want to find dy/dx, and then find when it equals 1 (the tan of 45).

Note: I am assuming it's an anticlockwise angle. If it were a clockwise angle then the tan would be -1.
Original post by ghostwalker
Yes. You need the tangent to make an angle of 45 with the positive x-axis.

And since the tan of that angle is equal to the derivative, you want to find dy/dx, and then find when it equals 1 (the tan of 45).

Note: I am assuming it's an anticlockwise angle. If it were a clockwise angle then the tan would be -1.


okay thankyou :smile:
ImageUploadedByStudent Room1449866499.386147.jpg



Can anyone help with part c I'm not sure how to go about it


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ImageUploadedByStudent Room1449866558.233948.jpg

This is what I have for b not sure how to do part a also


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Original post by Misshussain23
ImageUploadedByStudent Room1449866499.386147.jpg



Can anyone help with part c I'm not sure how to go about it


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You need the answer to (a) first.

What value does y take when a curve crosses the x-axis?

What value does x take when a curve crosses the y-axis?
Original post by Muttley79
You need the answer to (a) first.

What value does y take when a curve crosses the x-axis?

What value does x take when a curve crosses the y-axis?


but i'm not sure how to do a :/
Original post by Misshussain23
but i'm not sure how to do a :/


That was a hint for part (a)
oh okay thanksss
Original post by Muttley79
That was a hint for part (a)


when x=1 y=0 when x=-1 y=4 ?
Original post by Misshussain23
when x=1 y=0 when x=-1 y=4 ?


y = 0 gives more than one value of x.

x = 0 gives y = (0 - 1)(0 + 2) = ......

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