Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
roots of a trinomial
\[ax^3+bx^2+cx+d=0\]
let the roots be \(p,q,r\)
When \(x\) is equal a root the equation equals zero
\[(xp)(xq)(xr)=0\]
\[(xp)(x^2(q+r)x+qr)=0\]
\[x\left(x^2(q+r)x+qr\right)p\left(x^2(q+r)x+qr\right)=0\]
\[\left(x^3(q+r)x^2+(qr)x\right)\left(px^2p(q+r)xqpr\right)=0\]
\[x^3(p+q+r)x^2+(qr+pq+pr)xpqr=0\]
comparing with
\[x^3+\frac bax^2+\frac cax+\frac da=0\]
\[(p+q+r)=\frac ba\qquad\text{the sum of the roots is } \frac ba\]
\[(qr+pq+pr)=\frac ca\qquad\text{sum of products of pairs of the roots is } \frac ca\]
\[pqr=\frac da\qquad \text{the product of the roots is} \frac da \]
 one year ago
 one year ago
roots of a trinomial \[ax^3+bx^2+cx+d=0\] let the roots be \(p,q,r\) When \(x\) is equal a root the equation equals zero \[(xp)(xq)(xr)=0\] \[(xp)(x^2(q+r)x+qr)=0\] \[x\left(x^2(q+r)x+qr\right)p\left(x^2(q+r)x+qr\right)=0\] \[\left(x^3(q+r)x^2+(qr)x\right)\left(px^2p(q+r)xqpr\right)=0\] \[x^3(p+q+r)x^2+(qr+pq+pr)xpqr=0\] comparing with \[x^3+\frac bax^2+\frac cax+\frac da=0\] \[(p+q+r)=\frac ba\qquad\text{the sum of the roots is } \frac ba\] \[(qr+pq+pr)=\frac ca\qquad\text{sum of products of pairs of the roots is } \frac ca\] \[pqr=\frac da\qquad \text{the product of the roots is} \frac da \]
 one year ago
 one year ago

This Question is Closed

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351834318182:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351834441300:dw
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
what about complex solutions
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351834556416:dw
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
i guess a trinomial always has at least one real root
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351834728740:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351834848416:dw
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
if the trinomial has real coefficients, then complex roots occur in pairs, hence it must have atleast 1 real solution .
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351834939890:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351835035013:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351835192802:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351835381933:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
this is the general for all norder polynomial equation.
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
notice the sign change everytime, product of all roots = \( (1)^n a_0/a_n \)
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351835549510:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
I should mention that there are all real and complex roots in formulas.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351839125496:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351839193349:dw
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.