Let $P(x) = a_{1998}X^{1998} + a_{1997}X^{1997} +...+a_1X + a_0$ be a polynomial with real coefficients such that $P(0) \ne P (-1)$, and let $a, b$ be real numbers. Let $Q(x) = b_{1998}X^{1998} + b_{1997}X^{1997} +...+b_1X + b_0$ be the polynomial with real coefficients obtained by taking $b_k = aa_k + b$ ,$\forall k = 0, 1,2,..., 1998$. Show that if $Q(0) = Q (-1) \ne 0$ , then the polynomial $Q$ has no real roots.