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FP1 Finding roots exam question..

Given that 3+i is a root of the equation fx=0 where

f(x)=2x3+ax2+bx−10f(x) = 2x^3+ax^2+bx-10

(a) find the other two roots of the equation f(x) = 0..

(b) find the value of a and b..

(a) If 3+i is a root then I assume 3-i is a root too. How do i find the third root? I tried multiplying (x-3+i) and (x-3-i) but when i factorised that I just got 3+or-i again.. :s-smilie: I'm a bit confused.. help?
Reply 1
Avatar for chris007as
chris007as
when you get the quadratic you multiply it by a real root (x+c) the will give you f(x)
Reply 2
Avatar for Rei
Rei
OP
14
Swayum
What do you get for (x - 3 + i)(x - 3 - i)?


x^2 - 6x + 10...
Reply 3
Avatar for Swayum
Swayum
18
Sorry, I don't know if there's something you're MEANT to do for the exam, but I would just look at it now and see that the third factor would obviously be (2x - 1). You need the 2x to get the 2x^3. You need the -1 to get the -10.
Reply 4
Avatar for Rei
Rei
OP
14
Swayum
Sorry, I don't know if there's something you're MEANT to do for the exam, but I would just look at it now and see that the third factor would obviously be (2x - 1). You need the 2x to get the 2x^3. You need the -1 to get the -10.


Oh ok, so am I right in thinking, to find a and b i subsitute 1/2, 3-i and 3+i and solve?
Reply 5
Avatar for Swayum
Swayum
18
You COULD, but I'd just expand out (x^2 - 6x + 10)(2x - 1) and compare coefficients. Much faster.
Product of roots = 102\frac{10}{2}
Reply 7
Avatar for Tallon
Tallon
16
if product of roots = 5 then multiply out:
(3+i)(3-) = 9-i^2 = 10
10 * something = 5
something = 5/10 = 0.5

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