Question

If x-2 is a factor of x3 +ax2+bx+16 and ,a-b=6.find the value of a and b

Answer 1

Answer:

a= -2

b= -8

Step-by-step explanation:

x-2=0

x=2

By Remainder Theorem...

x3+ax2+bx+16=0

2^3+a (2)^2+b (2)+16=0

8+4a+2b+16=0

24+4a+2b=0

4a+2b= -24

2 (2a+b)= -24

2a+b= -12........(1)

BY THE PROBLEM....

a-b=6........(2)

Now,

add the equations 1 and 2

2a+b= -12

a-b= 6

..................

3a= -6

.............

a= -6/3

a= -2

substitute a in the equation 2

a-b=6

-2-b= 6

-2-6 =b

b= -8

Therefore,

a= -2

b = -8

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