Question

f(x)= 2x^3 - 5x^2 - 9x + 18, where a is a constant.
Given that (x-3) is a factor of f(x),
(b) Factorise f(x) completely.

Given that
g(y)= 2(3^3y) - 5(3^2y) - 9(3^y) + 18
(c) Find the values of y that satisfy g(y)=0, giving your answers to 2 d.p. where appropriate.

Answer 1

Step-by-step explanation:

a) 54-45+3a+18=0 3a+27=0 3a=-27 and thus a=-9b) 2x^3 – 5x^2 -9x + 18 = (x-3) (2x^2 +bx-6)to find b ; collect the x^2 terms so bx^2-6x^2=-5x^2 and thus b=1c) when comparing f(y) and f(x) we see that x=3^2yf(x)=(x-3) , (2x-3) , (x+2)so x = 3 x=3/2 and x=-2when x=3 , y=1when x=-2 , no solution and when x=2/3 , take logs woth base of 3 and you get y=0.3690