Question

help me in this pls​

Answer 1

Answer:

a= -3

b= -13

Step-by-step explanation:

p(x)=x³+ax²+bx+6

(x-2) is a factor.

Therefore x-2=0

                 x=2

Therefore 2 is the zero of p(x).

p(2)=(2)³+a(2)²+b×2+6=0

     =8+4a+2b+6=0

      =4a+2b= -14

      =2a+b= -7                 ...............................Equation 1

When p(x) is divided by (x-3) the remainder is 3.

So when x=3 the p(x) has the remainder 3

p(3)=(3)³+a(3)²+b×3+6=3

     =27+9a+3b+6=3

     =9a+3b= -30

     =3a+b= -10                          ................Equation 2

On subtracting Equation 1 with 2

We get,

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

-a=3

a= -3

On putting the value of a= -3 in equation

We get,

2×-3+b= -7

b= -7-6

b= -13