Determining the number of roots in the given equations.

1. Without solving the equation determine the number of roots (real, different, same, imaginary):

a) 2x^2+7x-14=0

b) do the same for 2x^2-3x+10=0

c) e^2x+5=ln 125

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... roots.
b) Compute the determinant: b^2-4ac=(-3)^2-4(2)(10)=9-80=-71<0
Thus the equation ...