Find the complex zeros of the polynomial function. Write f in factor.pdf
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The document details the process of finding the complex zeros of the polynomial function f(x) = x^4 + 17x^2 + 16. By substituting y = x^2 and solving the resulting quadratic equation, the complex roots are determined to be x = -i, i, 4i, and -4i. The polynomial can be expressed in factored form based on these roots.
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Find the complex zeros of the polynomial function. Write f in factor.pdf
- 1. Find the complex zeros of the polynomial function. Write f in factored form. f(x)=x^4+17x^2+16 Solution f(x)=x^4+17x^2+16 Let x^2 = y .So, y^2 +17y +16 =0 Solve the quadratice equation by using te formula: x= (-b +/- sqrt(b^2 -4ac) )/2a y = ( -17 +/- sqrt(17^2 -4*16) )/2 y = -16 , -1 Now x^2=y : x^2 = -16 ---> x = +/- 4i x^2 = -1 -----> x = +/- i Roots : x= -i , i , 4i ,-4i