Question

If r and s be the remainder when the polynomials
(x³+2x²-5ax-7) and (x³+ax²-12ax+16 are divy by (x+1) and (x+2) respectively and 2r +s=6
Then find the value of a =?

Answer 1

Hi there!

P(x) = x³+2x²-5ax-7

Putting the value of x =-1 from (x+1)

P (-1) = (-1)³+2(-1)²-5a(-1) -7
         
= -1+ 2+ 5a- 7
       
= -6+5a

Q(x) = x³+ax²-12a+6

Putting the value of x = 2 from (x-2)

Q(2) = (2)³+ a(2)²- 12(2) +6
     
= 8+ 4a- 24+ 6 
     
= -10+ 4a

Given that,
2r + s= 6  

2(-6+5a) + (-10+4a) = 6

-12+10a-10+4a = 6

-22+ 14a = 6
     
14a = 6+ 22
             
a = 28/14
              
a = 2

Therefore,
Value of 'a' is 2.

[ Thank you! for asking the question. ]
Hope it helps!