Solve the following equation by identifying all of its roots including any imaginary numbers and multiple roots (x^2-1)(x^2+2)(x+3)(x-4)(x+1)=0

Use the quadratic formula to solve the equation. if necessary, round to the nearest hundredth. x^2 - 8 = -6x a. –7.12, 1.12 b. 7.12, –1.12 c. 7.12, 1.12 d. –7.12, –1.12

What are the solutions of the equation? z^2 + 11z + 24 = 0 a. 8, -3 b. 8, 3 c. -8, -3 d. -8, 3

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .