Question

If (x-3)and (x-1÷3) are both factors of ax^2+5x+b,show that a=b?

Answer 1

Here is your answer


x=3 and x=1/3

p(x)=ax²+5x+b
p(3) = a×3×(3)²+5×3+b

= 27a+15+b = 0
= 27a+b=-15_(1)

p(1/3) = a×(1/3)²+5×1/3+b
= a/9 + 5/3 + b = 0
= a + 15 + 9b = 0
= a + 9b = -15_(2)
from (1)
b = -15-27a
put value of b in (2)
a + 9b = -15
-15-27a +9a = -15
-18a = -15+15

a = 0
put a = 0 in
b = -15-27a = -15-27×0 = -15


Hope it helps you ^_^