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Question Number 212152 by RojaTaniya last updated on 04/Oct/24

Answered by som(math1967) last updated on 04/Oct/24

x^3 +ax+b=(x+c)(x−1)(x−2) put x=1 a+b=−1 ....case1 put x=2 2a+b=−8 ∴ a=−7,b=6 now x^3 −7x+6 =(x−1)(x^2 +x−6) =(x−1)(x−2)(x+3) ∴ c=3 log_(a+b+c) (b+c−a)^(a−b−c) log_2 (16)^(−16) [b+c−a=6+3−(−7)=16] =−16×4log_2 2=−64

x3+ax+b=(x+c)(x−1)(x−2)putx=1a+b=−1....case1putx=22a+b=−8∴a=−7,b=6nowx3−7x+6=(x−1)(x2+x−6)=(x−1)(x−2)(x+3)∴c=3loga+b+c(b+c−a)a−b−clog2(16)−16[b+c−a=6+3−(−7)=16]=−16×4log22=−64

Commented by RojaTaniya last updated on 04/Oct/24

Sir, (b+c−a)=16, answer will be −64

Sir,(b+c−a)=16,answerwillbe−64

Commented by som(math1967) last updated on 04/Oct/24

thank you , I corrected

thankyou,Icorrected

Answered by Rasheed.Sindhi last updated on 04/Oct/24

x^3 +ax+b=(x+c)(x^2 −3x+2) x^3 +ax+b=x^3 −3x^2 +2x+cx^2 −3cx+2c =x^3 +(c−3)x^2 +(2−3c)x+2c c−3=0⇒c=3 a=2−3c=2−3(3)=−7 b=2c=2(3)=6 log_((−7+6+3)) (6+3+7)^(−7−6−3) =log_2 16^(−16) =(−16)log_2 16=−64

x3+ax+b=(x+c)(x2−3x+2)x3+ax+b=x3−3x2+2x+cx2−3cx+2c=x3+(c−3)x2+(2−3c)x+2cc−3=0⇒c=3a=2−3c=2−3(3)=−7b=2c=2(3)=6log(−7+6+3)(6+3+7)−7−6−3=log216−16=(−16)log216=−64

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