Question and Answers Forum

All Questions      Topic List

Relation and Functions Questions

Previous in All Question      Next in All Question      

Previous in Relation and Functions      Next in Relation and Functions      

Question Number 145294 by imjagoll last updated on 04/Jul/21

Given a polynomial   p(x)=x^4 +4x^3 +(2p+2)x^2 +(2p+5q+2)x+3q+2r.  If p(x)= (x^3 +2x^2 +8x+6)Q(x)   then what the value of    (p+2q)r .

Givenapolynomialp(x)=x4+4x3+(2p+2)x2+(2p+5q+2)x+3q+2r.Ifp(x)=(x3+2x2+8x+6)Q(x)thenwhatthevalueof(p+2q)r.

Answered by Rasheed.Sindhi last updated on 04/Jul/21

p(x)=x^4 +4x^3 +(2p+2)x^2 +(2p+5q+2)x+3q+2r.  If p(x)= (x^3 +2x^2 +8x+6)Q(x)   (p+2q)r =?                                            _(−)   Let Q(x)=x+k  Given: D(x)=x^3 +2x^2 +8x+6  We can also consider:  D(x)=x+k  &  Q(x)=x^3 +2x^2 +8x+6  By synthetic division :   determinant (((−k)),1,(    4),(2p+2),(2p+5q+2),(3q+2r)),(,,(−k),(    ...),(       ...),(   ...)),(,1,(   2),(   8),(       6),(    0)))   4−k=2⇒k=2   determinant (((−2)),1,(    4),(2p+2),(2p+5q+2),(3q+2r)),(,,(−2),(  −4),(     −16),( −12)),(,1,(  2),(    8),(        6),(    0)))   2p+2−4=8⇒p=5  2p+5q+2−16=6  2(5)+5q=20⇒q=2  3q+2r−12=0  3(2)+2r=12⇒r=3  (p+2q)r =( 5+2(2) )(3)=27

p(x)=x4+4x3+(2p+2)x2+(2p+5q+2)x+3q+2r.Ifp(x)=(x3+2x2+8x+6)Q(x)(p+2q)r=?LetQ(x)=x+kGiven:D(x)=x3+2x2+8x+6Wecanalsoconsider:D(x)=x+k&Q(x)=x3+2x2+8x+6Bysyntheticdivision:k)142p+22p+5q+23q+2rk.........128604k=2k=22)142p+22p+5q+23q+2r241612128602p+24=8p=52p+5q+216=62(5)+5q=20q=23q+2r12=03(2)+2r=12r=3(p+2q)r=(5+2(2))(3)=27

Commented by imjagoll last updated on 04/Jul/21

yes

yes

Answered by liberty last updated on 04/Jul/21

by Horner′s theorem  d(x)=x^3 +2x^2 +8x+6=0  ⇒x^3 =−2x^2 −8x−6    determinant ((∗,1,4,(2p+2),(2p+5q+2),(3q+2r)),((−2),∗,(−2),(−8),(−6),∗),((−8),∗,∗,(−4),(−16),(−12)),((−6),∗,∗,∗,∗,∗),(∗,1,2,(2p−10),(2p+5q−20),(3q+2r−12)))   we get  { ((2p−10=0→p=5)),((10+5q−20=0→q=2)),((6+2r−12=0→r=3)) :}  then (p+2q)r=(5+4)×3=27

byHornerstheoremd(x)=x3+2x2+8x+6=0x3=2x28x6142p+22p+5q+23q+2r22868416126122p102p+5q203q+2r12weget{2p10=0p=510+5q20=0q=26+2r12=0r=3then(p+2q)r=(5+4)×3=27

Commented by imjagoll last updated on 04/Jul/21

yes

yes

Terms of Service

Privacy Policy

Contact: info@tinkutara.com