# Roots of Polynomials

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#1
https://imgur.com/a/YImuFvR
0
2 years ago
#2
(Original post by Y12_FurtherMaths)
https://imgur.com/a/YImuFvR
looks ok to me
0
#3
(Original post by mqb2766)
looks ok to me
Cheers
0
2 years ago
#4
LMAO I'm on the same board, I remember doing this last year.

Yeah you want to start by establishing what you know about the first polynomial. I.e that a + b + c = -2, ab + bc + ac = 1 and abc = -3.

Now you know for this second polynomial that that the sub of the roots, ab + bc + ac = -p, we know that this is equivalent to one of the statements in the first polynomial so we know that -p = 1, so p = -1

Now for the product, of all 3, that being a^2b^2c^2 which is the same as (abc)^2, is equal to -r, so (-3)^2 = 9 = -r and so r = -9

The sum two at a time being ab^2c + a^2bc + abc^2 = q, taking out the factor of abc we get abc(b + a + c) = q, and given abc = -3, and a + b + c = -2, we get -3(-2) = q, so 6 = q and the full polynomial is x^3 - x^2 + 6x - 9 = 0, which is the same you got so it looks good to me.
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#5
(Original post by thotproduct)
LMAO I'm on the same board, I remember doing this last year.

Yeah you want to start by establishing what you know about the first polynomial. I.e that a + b + c = -2, ab + bc + ac = 1 and abc = -3.

Now you know for this second polynomial that that the sub of the roots, ab + bc + ac = -p, we know that this is equivalent to one of the statements in the first polynomial so we know that -p = 1, so p = -1

Now for the product, of all 3, that being a^2b^2c^2 which is the same as (abc)^2, is equal to -r, so (-3)^2 = 9 = -r and so r = -9

The sum two at a time being ab^2c + a^2bc + abc^2 = q, taking out the factor of abc we get abc(b + a + c) = q, and given abc = -3, and a + b + c = -2, we get -3(-2) = q, so 6 = q and the full polynomial is x^3 - x^2 + 6x - 9 = 0, which is the same you got so it looks good to me.
Appreciate it! We’re actually on AQA and we have a test next Friday so our teacher didn’t want us to do AQA questions for practice incase any of them came up on the test so he handed us OCR ones.
0
2 years ago
#6
What's the question right at the end talking about? These exam boards need to extinct, ffs!
0
#7
(Original post by ftfy)
What's the question right at the end talking about? These exam boards need to extinct, ffs!
Finding the square roots of 24 10i?
Last edited by Y1_UniMaths; 2 years ago
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