The complex zeros of f 1x2 = x4 + 1 For the function f1x2 = x4 + 1: (a) Factor f into the product of two irreducible quadratics. (Hint: Complete the square by adding and subtracting 2x2 .2 (b) Find the zeros of f by finding the zeros of each irreducible quadratic.

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The complex zeros of f 1x2 = x4 + 1 For the function f1x2 = x4 + 1:  (a) Factor f into the product of two irreducible quadratics. (Hint: Complete the square by adding and  subtracting 2x2  .2  (b) Find the zeros of f by finding the zeros of each irreducible quadratic.

pripravyf · Accepted Answer

Step 1 Given : f(x)=x4+1 f(x)=x4+2x2+1−2x2(Add and subtract 2x2) =(x2+1)2−2x)2 f(x)=(x2+1+2x)(x2+1−2x (usin⁡gα2−b2+(a+b)(a−b))

Tapanuiwp · Accepted Answer

b) To find the zeros of f:  We find the zeroes of x2+1+2x=0andx2+1−2x=0  Using quadratic formula,  x=−b±b2−4ac2a  x=−2±(22)−4(1)(1)2(1),−(−2)±(22)−4(1)(1)2(1)  x=−2±2−42,2±2−42  x=−2±i22,2±i22  Hence, there are no real zeroes. And the complex zeroes of f(x)=x4=1  are  x=−2±i22andx=2±i22

The complex zeros of f 1x2 = x4 + 1

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