Let `a, b, c` be real numbers, `a != 0.` If `alpha` is a zero of `a^2 x^2+bx+c=0, beta` is the zero of `a^2x^2-bx-c=0 and 0 , alpha < beta` then prove that the equation `a^2x^2+2bx+2c=0` has a root `gamma` that always satisfies `alpha < gamma < beta.`