Question

let p and q are the remainders when the polynomial x3 +2x2-5ax-7and x3+ax2-12x+6 are divided by x+1 and x-2 respectively if 2p+q=6 find a​

Answer 1

so

here you dont worry about it is very good question

Answer 2

Answer:

a=2

Step-by-step explanation:

let f(x)= x3 +2x2-5ax-7

and g(x)= x3+ax2-12x+6

when f(x) is divided by x+1

the remainder is p

so f(-1)=p

(-1)^3+2(-1)^2-5a(-1)-7=p

-1+2+5a-7=p

p=5a-6--------------(1)

also when g(x) is divided by x-2

the remainder is q

g(2)=q

(2)^3+a(2)^2-12*2+6=q

8+4a-24+6=q

q=4a-10-------------(2)

No given that

2p+q=6

putting value from (1) and (2)

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

10a-12+4a-10=6

14a=6+12+10=28

a=28/14=2

a=2