Need help on Question - Cambridge EX 4F Q5 (1 Viewer)

[slix_88]

Hi guys...Im stuck on one question which is based on polynomials. The question asks...

Show that x=1 and x=-2 are zeroes of P(x), and use the sum and prodcut of zeroes to find the other one or two zeroes. Note any multiple zeroes:
b) P(x) = 2x^3 + 3x^2 - 3x - 2
d) P(x) = 3x^4 - 5x^3 - 10x^2 + 20x - 8

I know they may seem easy to many ppl, but I just don't know what the sum and product of the zeroes are? Please including all your working out, including explanation.

Help is much appreciated!

 

[haboozin]

Hi guys...Im stuck on one question which is based on polynomials. The question asks...

Show that x=1 and x=-2 are zeroes of P(x), and use the sum and prodcut of zeroes to find the other one or two zeroes. Note any multiple zeroes:
b) P(x) = 2x^3 + 3x^2 - 3x - 2
d) P(x) = 3x^4 - 5x^3 - 10x^2 + 20x - 8

I know they may seem easy to many ppl, but I just don't know what the sum and product of the zeroes are? Please including all your working out, including explanation.

Help is much appreciated!

well a poly is eg ax^3 + bx^2 + cx + d

now sum of roots 1 at time = -b/a
sum of roots 2 at time = c/a
sum of roots 3 at time (which in this case becomes the product of the roots) = -d/a

note how it goes -+-

now since 1 and -2 are roots then

by sum of roots 1 at time

1 + -2 + B = -3/2

and thats how the 3rd root is found in b


for d: u do the same but it will be

1 -2 + B + A = 5/3 ........(1)

and product of the roots (which is always the last thing divided by a)

-2AB = 8/3 ........(2)

now solve 1 and 2 silmuntaniously.

 

[slix_88]

Thnx a lot for your help!!