polynomials questions (1 Viewer)

[NizDiz]

Hey guys, want to make sure I've got these 2 questions correct.

1. 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. Not sure how to do this, please help!


2. Two of the roots of the equation x^3 + px^2 + qx +r =0 are equal in magnitude but opposite in sign.
(a) Show that x= -p is the other root
(b) Show that r = pq

Fine with part (a), did part (b), but my teacher said I did it wrong. Someone please help me, thanks

 

[HeroicPandas]

Hey guys, want to make sure I've got these 2 questions correct.

1. 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. Not sure how to do this, please help!


2. Two of the roots of the equation x^3 + px^2 + qx +r =0 are equal in magnitude but opposite in sign.
(a) Show that x= -p is the other root
(b) Show that r = pq

Fine with part (a), did part (b), but my teacher said I did it wrong. Someone please help me, thanks

1. Since the the degree of the polynomial is 3, it'll have 3 real roots



"One of the roots....is equal to the sum of the other 2 roots"



Use sum of roots one/two at a time and product of roots and use simultaneous equations

2. Let P(x) = x^3 + px^2 + qx +r =0

From part 1 and using the factor theorem, P(-p) = 0

Therefore, -p^3 + p^3 -pq + r = 0

Therefore, r = pq

goodluck

 

[NizDiz]

thanks mate helps a lot!