1. ## polynomial cubic roots

Solve the equation 4xcubed + 32xsquared + 79x + 60 = 0 given that one root is equal to the sum of the other two

Here is my working out so far

Let the roots be alpha, beta and gamma
alpha + beta = gamma

AND you know that

alpha + beta + gamma = (-b/a) = (-8)
alpha x beta x gamma = (-d/a) = (-15)
alphabeta + alphagamma + betagamma = (79/4)

i would realli like some help on how to proceed from here ?
i just need to find wat alpha, beta and gamma are and am having alot of difficulty ><"" thankyouu for any help !! =D

2. Originally Posted by THSKluv
Solve the equation 4xcubed + 32xsquared + 79x + 60 = 0 given that one root is equal to the sum of the other two

Here is my working out so far

Let the roots be alpha, beta and gamma
alpha + beta = gamma

AND you know that

alpha + beta + gamma = (-b/a) = (-8)
alpha x beta x gamma = (-d/a) = (-15)
alphabeta + alphagamma + betagamma = (79/4)

i would realli like some help on how to proceed from here ?
i just need to find wat alpha, beta and gamma are and am having alot of difficulty ><"" thankyouu for any help !! =D

let a , b and y be 3 roots of this cubic equation .

a+b+y=-8 ( the sum of roots ) --- 1

aby=-15 ( the product of roots ) --- 2

a=b+y ( one roots is the sum of the other 2 roots ) -- 3

from 1 , b+y=-8-a

substitute into 3 , a=-8-a , a=-4

Then go back to 1 and 2 again .

-4+b+y=-8

b+y=-4 -- 4

-4by==-15

by=15/4 -- 5

then u can solve the simultaneous equation (4 and 5) to get b and y .

Note that both b and y can be -2.5 and -1.5 but not at the same time . Lets say if you put b=-2.5 , then y has to be -1.5 and vice versa .

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# sum and product of roots of cubic equation

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