Polynomial question (1 Viewer)

[jockrussell]

Consider the equation
x^3+6x^2-x-30=0.
One of the roots of this equation is equal to the sum of the other two roots.
Find the values of the three roots.

Its been a while since i done polynomials, and i cant think of how to do this.
Please help.

 

[lolokay]

write it as (x+a)(x+b)(x+a+b) then expand and equate coefficients. There might be a quicker way if you know the root identity things but I cbf learning them

 

[foram]

Consider the equation
x^3+6x^2-x-30=0.
One of the roots of this equation is equal to the sum of the other two roots.
Find the values of the three roots.

Its been a while since i done polynomials, and i cant think of how to do this.
Please help.

P(2) = 0

Therefore, (x -2) is a factor.

P(x) = (x -2)(x^2 +8x +15)
= (x -2)(x +3)(x +5)

The roots are

x= 2, -3, -5

 

[tacogym27101990]

your meant to let the roots be a, b , a+b and use the relationships between the roots and coefficients in this kind of question
but factor theorem is much quickerer

 

[jockrussell]

Thanks guyz, that was easier than i was making it.

 

[3unitz]

let roots be A, B, A + B

A + B + A + B = -6
A + B = - 3

AB(A+B) = 30
AB = -10

A^2 + 3A - 10 = 0
(A + 5)(A - 2) = 0

roots: 2, -5, -3