Let $f\in C[a,b]$ be differentiable in $(a,b)$. If $f(a)=f(b)=0$ then prove that for any real number $\alpha$ $\exists$ $x\in (a,b)$ such that, $$f'(x)+\alpha f(x)=0.$$

Clearly,this is a problem of Roll's theorem. First consider the function $\phi (t)$
 such that $\phi$ is continuous on $[a,b]$
 & differentiable on $(a,b)$ & $\phi (a)=\phi (b)$ & such that $\phi'(t)=f'(t)+\alpha f(t)$. But I can't construct such a function. Please help on construction such a function $\phi$.