Question

find the value of a and b in p(x) = 3x^3-9x^2+ax+b p(2)=19 and p(-1)=12​

Answer 1

putting the value of 2 in the equation,we have--

p(2)=3(2)^3-9(2)^2+2a+b

= 24-36+2a+b

=12+2a+b

19=12+2a+b

19-12=2a+b

2a+b=7

putting the value of -1 in the equation,we have--

p(-1)=3(-1)^3-9(-1)^2+(-1)a+b

=-3 -9-a+b

=-12-a+b

12=-12-a+b

12+12=-a+b

-a+b=24

now ,

2a+b=7

b=7-2a

Substituting the value of b in the equation, we have

-a+7-2a=24

7-3a=24

7-24=3a

-17=3a

-17/3=a

Hence,a=-17/3

-a+b=24

-(-17/3)+b=24

b=24-17/3

b=55/3