Question

qus. no. 21 and 22 plzz give the answer

Answer 1

Question 21

Let f(y)= y^3+2y^2-5ay-7
When f(y) is divided by (y+1),
Remainder=f(-1)

But remainder=A
i.e. A=f(-1)
A=(-1)^3+2×(-1)^2-5a(-1)-7
A=-1+2+5a-7
A=5a-4

Let g(y)= y^3+a^2-12y+6
When g(y) is divided by (y-2),
Remainder=g(2)

But remainder=B
i.e. B=g(2)
B=2^3+a^2-12×2+6
B=8+a^2-24+6
B=a^2-10

According to question,
2A+B=6
i.e., 2(5a-4)+a^2-10=6
10a-8+a^2-10=6
a^2+10a-18-6=0
a^2+10a-24=0
a^2+12a-2a-24=0
a(a+12)-2(a+12)=0
(a-2)(a+12)=0

a-2=0 or a+12=0
a=2 or a=-12