Question

Explain why 3x^2+kx-1 is never always positive for any value of k

Answer 1

Hello : 
(3x²+kx-1) is a quadratic polynome when : a =3  , b=k , c= -1
the discriminat  Δ = b²-4ac ≥ 0 because ac = -3 < 0
-4ac >0  and b²≥0
the  quadratic polynome has :2 solutios or 1 solution (Change of sign)
conclusion :   is never always positive for any value of k