Question

Find the values of a and b ,so that the polynomial p(x)=3x^3+ax^2-13x+b is divisible by x^2-2x-3 please plz

Answer 1

Answer:

Let p(x) = x3 – ax2 – 13x + b be the given polynomial.

If (x – 1) and (x + 3) are the factors of p(x) then

p(1) = 0

and p(-3) = 0

p(1) = (1)3 – a(1)2 – 13(1) + b = 0

= 1 – a – 13 + b = 0

a – b = -12

p(-3) = (- 3)3 – a(- 3)2 - 13(- 3) + b = 0

= - 27 – 9a + 39 + b = 0

9a – b = 12 ….(2)

Solving (1) and (2) we get

a = 3

and b = 15

Answer 2

Answer:

let p(x)=3-a×2-13×+b be the given polynomial

if(×-1)and(x+3)are the factors of p (x) then

p(1)=0

and p(-3)=0

p(1)=(1)3 -a(1)2-13(1)+b=0

1-a-13+b=0

a-b=-12

p(-3)3-a(-3(2-13(-3)+b=0

-27-9a+39+b=0

9a-b=12....(2)

a=3

b=15