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
Originally Posted by THSKluv
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 .
b+y=-4 -- 4
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 .