The roots of the polynomial equation are: x1 = -2 and x2 = 16
The polynomial equation is given as:
\(x^2 - 14x - 32 = 0\)
Expand the equation
\(x^2 - 16x + 2x - 32 = 0\)
Factorize the equation
\(x(x - 16) + 2(x - 16) = 0\)
Factor out x - 16, in the equation
\((x + 2)(x - 16) = 0\)
Solve for x
x = -2 or x = 16
Hence, the roots of the polynomial equation are: x1 = -2 and x2 = 16
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