Question

Please solve this problem ?​

Answer 1

Answer:

The value of a and b are -3 and -1 respectively.

Step-by-step explanation:

Given that (x-2) is a factor of polynomial

P(x)=x^3+ax^2+bx+6

Also when divided by (x - 3) leaves a remainder 3.

we have to find the value of a and b.

As 2 is the zero of the polynomial therefore by remainder theorem

P(2)=0

2^3+a(2)^2+2b+6=0

8+4a+2b+6=0

4a+2b+14=0

2a+b=-7     →   (1)

\text{Also the polynomial }x^3+ax^2+bx+6\text{ when divided by (x - 3) leaves a remainder 3}

∴ P(3)=3

3^3+a(3)^2+3b+6=3

27+9a+3b+6=3

9a+3b+33=3

3a+b=-10     →   (2)

Solving (1) and (2), we get

Subtracting equation (2) from (1)

2a+b-3a-b=-7-(-10)

-a=3

a=-3

2a+b=-7

2(-3)+b=-7

b=-7+6=-1

Hence, the value of a and b are -3 and -1 respectively.

Step-by-step explanation:

Answer 2

Answer:

oh sry bro i am not that much big brain