How to solve polynomial equation?

Question

kindly explain me how to find zero of polynomial equation with non real coefficient. I know all the rules and methods for finding zero of polynomila with real coefficient . For quadratic (-b +/-sqrt(b^2-4ac))/2a shall work even for abc non real. so if factor method may kindly be provided that is general method

I am sorry that this has not been understood properly. I am looking for solution of an equation say

x^3+ i = 0
where constant is i and not real. This is very trivial as x^2 and x are missing but how to go about it. in general

Answer 1

Assuming abc are all non-real coefficients

(-(bi) ± sqrt((bi)^2 - 4(ai)(ci)))/(2(ai))
(-bi ± sqrt((b^2 * i^2) - (4ac * i^2)))/(2(ai))
(-bi ± sqrt((b^2 * -1) - (4ac * -1)))/(2ai)
(-bi ± sqrt(-b^2 + 4ac))/(2ai)
(-bi ± sqrt(-(b^2 - 4ac)))/(2ai)
(-bi ± isqrt(b^2 - 4ac))/(2ai)

Multiply top and bottom by "i"

(-(-b) ± sqrt(b^2 - 4ac))/(2a)

(b ± sqrt(b^2 - 4ac))/(2a)

To really make sure i have everything correct, i am going to need to know what "a", "b", and "c" are.

If you go to www.quickmath.com and type in sqrt(-1) instead of "i", it will tell you what the x-intercepts are.

Answer 2

when you factor, whats important is the A & C of the charastic equation ax^2 + bx + c
when you FOIL (first*first, outside*outside, inside*inside, last*last)the first*first is the a .... the last*last is the c .... the inside and outside terms are "combinable" or they are of like terms...
when a=1... you find factors of c that add to b ....
take c = 72 factors of 1,2,3,4,6,8,9,12,18,24,36,72
b can become (1,72)=73 ... (2,36)=38...(3,24)=27...and so on...

x^2 + 13x+ 36 .... factors of 36 that add to 13 (x+9) (x+4)
( so the zero's are (-9,-4)
when you solve quadradic equation, you are given the vertex (-b/2a) and the distance from the vertex to find the zero's (b^2-4ac)^1/2 .. some like this method because it's fail-proof

(trick is ... if the discriminate is a perfect square... it can be factored with abc's of foil....) discriminate is b^2-4ac

Answer 3

I know to solve polynomials by formula only cause i m still in 9th
standard i have that chapter but i practise, i feel that chapter is quite easy if we solve them perfectly and practise them if we know the formula.
If you need any help tell me i will help u because i score good marks in algebra!!!

Answer 4

Assume i = sqr(-1), calculation are same as before