Question

If x-3 and x-1/3 are both factors of of ax^2+5x+ab,then show that a=-3/2

Answer 1

since x-3 and x-1/3 are factors

(x-3)(x-1/3)= x²-3x-(1/3)x+1= x²-(10/3)x+1

to make -(10/3)x to 5x multiply by -(3/10)*5= -3/2

-(3/2)(x-3)(x-1/3)= -(3/2)x²+5x-3/2

Now by comparing -(3/2)x²+5x-3/2 with ax^2+5x+ab

you can see that a= -3/2