Question

if r and S be the remainders when polynomial x cube + 2 x square - 5a x minus 7 and x cube + ax square - 12a x + 6 are divided by (X+1) and (X-2) respectively and 2r plus s is equal to 6 find the value of a

Answer 1

p(x)=x³+2x²-5ax-7

g(x)=x+1

p(-1)=-1³+2(-1)²-5a(-1)-7

= -1+2+5a-7

=5a-6

∴remainder = 5a-6

r = 5a-6

p(x)=x³+ax²-12ax+6

g(x)=x-2

p(+2)=2³+2²a-12a(2)+6

=8+4a-24a+6

=14-20a

S=14 - 20a

acc to que

2r +S =6

2(5a-6) +14-20a = 6

⇒10a-12+14-20a =6

⇒-10a=6-2

⇒ -10a = 4

⇒ a= 4/-10

⇒a= -2/5

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