Question

let the polynomial x^3 - ax^2 + bx + 6 leave the remainder 3 when divided by x - 3. but it is divisible by x - 2. find the values of a and b.

Answer 1

Answer:

a value of a = -3 & b= -1

Step-by-step explanation:

Let p(x)=x³+ax²+bx+6

i ) it is given that , (x-2) is a factor of p(x) ,then

p(x)=0

=> 2³+a(2)²+b×2+6=0

=> 8+4a+2b+6=0

=> 4a+2b+14=0

Divide each term by 2 , we get

=> 2a+b+7=0 ---(1)

ii)It is given that, if p(x) divided by (x-3) leaves a remainder 3

=> p(3)=3

=> 3³+a(3)²+b×3+6=3

=> 27+9a+3b+6-3=0

=> 9a+3b+30=0

Divide each term by 3 , we get

=> 3a+b+10=0 ---(2)

Subtract equation (1) from equation (2) , we get

a + 3 = 0

=> a = -3

Now,

Substitute a=-3 in equation (1) , we get

2(-3)+b+7=0

=> -6+b+7=0

=> b+1=0

=> b = -1

Therefore,

value of a = -3 & b= -1