Question

For any real number α, the parabola fα(x)=2x2+αx+3α passes through the common point (a,b). What is the value of a+b?

Answer 1

for any \(\alpha\)?

Answer 2

if that includes \(\alpha =0\) then \(f(x)=2x^2\) and so \(f(a)=2a^2\) so \(a+b=a+2a^2\)

Answer 3

if it also works for \(\alpha =1\) then \(f(x)=2x^2+x+3\) so
\[f(a)=2a^2+a+3\] and so \(a+b=2a^2+2a+3\)

Answer 4

this tells you that \(a+b=2a^2+a\) and \(a+b=2a^2+2a+3\) thus
\[2a^2+2a+3=2a^2+a\] etc