Using the Rolle's theorem to prove by contradiction, how do you prove that there are two solutions without graphing?

Theorem 4.1.3/ Rolle's Theorem

THEOREM 4.1.3 ROLLE'S THEOREM Suppose that f is differentiable on the open interval (a, b) and continuous on the closed interval [a, b]. If f(a) and f(b) are both 0, then there is at least one number c in (a, b) for which f(c) = 0.Use Theorem 4.1.3 to prove that the equation 0 = to + 3t - 5t + 7 has no more than two solutions. (Hint: You may have to use the second derivative.)