Question

If ( x-3) and (x-1/3) are both factors of ax²+5x+b, then show that a=-3/2.

Answer 1

ax²+5x+b = 0.........(1)

(x–3)(x–⅓) = x²–(3+⅓)x+1
= x²–(10/3)x+1
x²–(10/3)x+1 = 0.........(2)

Sum of roots =-b/a= –5/a = 10/3
a = –5×(3/10) = –3/2

Product of roots = b/a = 1
a = b