Question

If f g are two polynomial functions where f (x) = (a X + 5)²

g (X) = 9 x² + 30 x+c-4 and f (x) = g (X), find the values of a and c

Answer 1

Hi,

a=3 and c=29

Explanation:

Let's expand the f(x) and identify the coefficients of f(x) and g(x)

`f(x)=(ax+5)^2=a^2x^2+10ax+25\\g(x)=9x^2+30x+c-4\\\\c-4=25\ \Longrightarrow\ c=29\\\\30x=10ax\ \Longrightarrow\ a=3\\\\a^2x^2=9x^2\ \Longrightarrow\ a=3\ or\ a=-3 \\\\So, \ a=3\ and\ c=29`