Question

Find if (x+2) (x+3) is a factor of x/\3+ax/\2+bx-12 find the value of a and b

Answer 1

if (x+2) (x+3) is a factor of x/\3+ax/\2+bx-12 , then
-2 and -3 are roots of equation.
Put -2 in the equation you'll get
-8+4a-2b-12=0
2a-b=10 ---- (i)

Put -3 in the equation
-27+9a-3b-12=0
3a-b=13 ----(ii)


from (i) and (ii)

a=3
b= -4