Question

Find the complex zeros of the following polynomial function. Write f in factored form. f(x) = x^4 + 26x^2 + 25 The complex zeros of f are (Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers as needed.) Use the complex zeros to factor f. f(x) = (Type your answer in factored form. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers as needed.)

          Find the complex zeros of the following polynomial function. Write f in factored form.
f(x) = x^4 + 26x^2 + 25
The complex zeros of f are 
(Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers as needed.)
Use the complex zeros to factor f.
f(x) = 
(Type your answer in factored form. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers as needed.)

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$Find the complex zeros of the following polynomial function. Write f in factored form. f(x) = x^4 + 26x^2 + 25 The complex zeros of f are (Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers as needed.) Use the complex zeros to factor f. f(x) = (Type your answer in factored form. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers as needed.)$

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Precalculus with Limits

Ron Larson 2nd Edition

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Solved by Expert Julie Silva

04/08/2022

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Find the complex zeros of the following polynomial function. Write f in factored form: f(x) = x^4 + 26x^2 + 25. The complex zeros of f are (Simplify your answer. Type an exact answer using radicals and i as needed. Use integers or fractions for any numbers as needed.) Use the complex zeros to factor f. f(x) = (Type your answer in factored form. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers as needed.)

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00:01 In this problem, we're given this function f of x, and we want to find the complex zeros for the following polynomial.

00:06 Okay.

00:07 So if we're trying to find the complex zeros, what we're doing is we're trying to figure out when does this polynomial function equal to zero.

00:14 So we can go ahead and solve this by factor.

00:17 So if this is going to factor, it's going to factor the two binomials.

00:20 Now the first term in each binomial has to the first term.

00:24 So because our middle term, it has x squared, they're both going to start with x squared, because x squared times x.

00:30 X squared is x to the 4.

00:31 So now we just have to find two numbers that multiply the 25 that add to 26.

00:36 Well, that would be 25 and 1.

00:38 So we would have plus 25 and plus 1.

00:41 Perfect.

00:42 So now that we have our factors, we can't actually factor any further, or unless they're going to be imaginary, which they will, now we're going to do is set both of our factors equal to 0.

00:52 So then we'll also have x squared plus 1 equal to 0.

00:55 So to solve the first equation, i'll subtract 5, 25 from both sides.

00:59 So we'll have x squared equal to negative 25.

01:07 And i apologize.

01:08 My computer's being a little slow at the moment.

01:10 So again, it's equal to negative 25.

01:13 And now we just have to take the square root of both sides...

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