Question

Find the value of a and b if x^3-ax^2-13x+b has x-1 and x+3 as factors

Answer 1

x-1=0
x=1
x^3-ax^2-13x+b=0
(1)^3-a(1)^-13×1+b=0
3-a-13+b=0
-a+b-16=0
-a+b=16. equation....1
x+3=0
x=-3
(-3)^3-a(-3)^2-13(-3)+b=0
27-a18+39+b=0
-a18+b+66=0
-a18+b=-66. equation... 2
from equation 1and2
-a+b=16
-a18+b=-66
__________on subtracting
a17=82
a=82/17
putting the value of a in equ. 1
-82/17 +b=-16
b=-16+82/17
b=-272+82/17
b=-190/17

Answer 2

x-1

x=1

x+3

x=-3

p(1)=x^3-ax^2-13x+b=g(-3)+x^3-ax^2-13x+b

1^3-a1^2-13+b=-3^3-a3^2-13x-3+b

1-a-13+b=-27-9a+39+b

-12-a+b=12-9a+b

-a+b+9a-b=12+12

-8a=24        (+b&-b cut off)

a=24/-8

a=-3

giving a value as -3 in the equation

1^3-3x1^2-13x1+b=0

1-3-13+b=0

-15+b=0

b=15