Question

the polynomial 6 x ki power 4 + 8 x cube + 17 X square + 21 X + 7 is divided by another polynomial 3 X square + 4 x + 1 the remainder comes out to be X + b find a and b

Answer 1

let x+b=a when6xpower4+8xcube+17xsquare+21x+7 the remainder is x+2

then,given remainder come outs to be x+b and quotient=2xsquare+0x+5

therefore,x+b=x+2

x+b=a

x+2=a

BY completing square method

2xsquare+0x=-5. use(1/2×b)square

(1/2×0)square

(o/2)square

(0)square

add (o)on both sides

2xsquare+0x+(o)square=-5+(0)square

(2x+0)square=-5+0

(2x+0)square=-5

2x+0=

$= + or - \sqrt{ - 5}$

2x=+root-5 or 2x=-root-5

x=+root-5/2 or x=-root-5/2

x can't be negative so x=root-5/2

x+2=a

root-5/2+2=a

root-5+4/2. (by LCM)

root-5+2 =a

therefore

the solution is a=root-5+2 &

b=2