Total no. of polynomials of the form x^3 +ax^2 +bx+c that are divisible by x^2 +1, where a,b,c∈1,2,3,....,10 is 1) 10 2) 15 3) 5 4) 8


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 32681 by rahul 19 last updated on 31/Mar/18

$T o t a l n o . o f p o l y n o m i a l s o f t h e f o r m$ $x^{3} + {a x}^{2} + b x + c t h a t a r e d i v i s i b l e b y$ $x^{2} + 1, w h e r e a, b, c \in 1, 2, 3, . . . ., 10 i s$ $1) 10$ $2) 15$ $3) 5$ $4) 8$
Commented by Rasheed.Sindhi last updated on 31/Mar/18

$If x^{2} + 1 is one factor of x^{3} + {a x}^{2} + b x + c$ $then other factor will be linear and of$ $type x + p .$ $(x^{2} + 1) (x + p) = x^{3} + {p x}^{2} + x + p$ $Comparing with given polynomial$ $we have b = 1 & a = c = p$ $Hence the given polynomial will be$ $of the form :$ $x^{3} + {a x}^{2} + x + a$ $Since a \in 1, 2, 3, . . ., 10 (Ten values)$ $Hence total number of polynomials$ $of the given form with given conditions$ $is 10$
Commented by rahul 19 last updated on 31/Mar/18

$t h a n k u s i r!$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum