$E_1: a+b+c=0$, if 1 is a root of $ax^2+bx+c=0$ .$E_2:b^2-a^2=2ac,$ if $\sin \theta, \cos \theta$ are the roots of $ax^2+bx+c=0$ Which of the following is true?

Question

(a) $E_1$ is true, $E_2$  is true. (b) $E_1$ is true, $E_2$  is false. (c) $E_1$ is false, $E_2$  is true. (d) $E_1$ is false, $E_2$  is false.