Use the Intermediate Value Theorem to show that f(x)=3x^3-x-1 has a zero in the interval [0,1]. Then approximate the zero rounded to two decimal places.
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Plot z=34i in the complex plane and find its absolute value.
Determine the number and nature of the roots of the equation in Exercise 67. Calculate the discriminant associated with the equation 6x2+5x+1=0.
Label each of the following statements as either true or false. 1. Every polynomial of positive degree over the complex numbers has a zero in the complex numbers.
The ________ ________ of ________ states that if f(x) is a polynomial of degree n (n > 0), then f hasat least one zero in the complex number system.
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.
The complex zeros of f(x) = x4 + 1 For the function f(x) = x4 + 1:(a) Factor f into the product of two irreducible quadratics. (Hint: Complete the square by adding and subtracting 2x2.) (b) Find the zeros of f by finding the zeros of each irreducible quadratic.
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