Question

f(x)=x3+kx2+hx+6, find the value of h & k when (x+1) (x-2) are factors

Answer 1

Answer:

Step-by-step explanation:

=Equ1 ; Equ2

F(-1)=-1+k-h+6 F(2)=8+4k+2h+6

Equate both to zero

Solve simultaneously

Equ1 Equ2

0=k-h+5 0=4k+2h+14

Sub 1 in 2

K=-12 h=17

Answer 2

Step-by-step explanation:

solve using the Chinese remainder theorem

for

x=-1

f(-1)=-1+k(-1)^2+h(-1)+6

f(-1)=0

k-h+5=0 ----(a)

for x=2

f(2)=8+4k+2h+6

f(2)=0

4k+2h+14=0

2k+h+7=0. -----(b)

simultaneously solve a and b

you will get

3k=-12

k=-4

put k =-4 in eq (a).

-4-h+5=0

h=1

the values of h and k are:

h=1. k=-4

checking:

F(2)=(2³)+(-4)(2²)+(1)(2)+6 =0

f(-1)=(-1³)+(-4)(-1²)+(1)(-1)+6=0