Question

Q30. If P(y) = y³ + ay² + by + 6 is divisible by (y – 2) and leaves remainder 3 when divided by (y - 3), then find the value of a and b.

Answer 1

Answer:

Please see the attachment

Answer 2

p(y)=y³+ay²+by+6

let,y=2

p(2)=(2)³+a(2)²+b(2)+6

=8+4a+2b+6

=4a+2b=-14→eq.1

=2a+b=-7

p(3)=(3)³+a(3)²+b(3)+6=3

=27+9a+3b+6=3

9a+3b=-30→eq.2

3a+b=-10

subtract eq.2-1

3a+b=-10

2a+b=-7

= a=-3

2a+b=-7

-6+b=-7

b=+6-7

b=-1