# Roots in equations

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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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#### Solution Preview

1 a) Compute the determinant: b^2-4ac=7^2-4(2)(-14)=49+112=161>0.

Thus the equation has two ...

#### Solution Summary

This shows how to determine the number of roots without solving an equation.

$2.49