Question

x+2,x+3 are factors of 2x^3 +ax^2+7x-b find values of a,b

Answer 1

x+2=0

x=-2

x+3=0

x=-3

2x³+ax²+7x-b=0

2(-2)³+a(-2)²+7(-2)-b=0

-16+4a-14-b=0

4a-b=30

2(-3)³+a(-3)²+7(-3)-b=0

-54+9a-21-b=0

9a-b=75→1

4a-b=30→2

subtract 1-2

9a-b=75

4a-b=30

5a=45

a=9

substitute in 1

9(9)-b=75

81-b=75

-b=-6

b=6

finally a=9,b=6