How many real fifth roots does 1024 have?
Question
How many real fifth roots does 1024 have?
Solution
1024 has one real fifth root. Here are the steps to find it:
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The fifth root of a number is the value that, when multiplied by itself four more times, gives the original number. In other words, if x^5 = 1024, then x is the fifth root of 1024.
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To find the fifth root of 1024, you can use the fifth root button on a scientific calculator, or raise 1024 to the power of 1/5.
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Doing this, you find that the fifth root of 1024 is 4.
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Therefore, 1024 has one real fifth root, which is 4.
Note: In the real number system, positive real numbers have only one real root for each positive integer exponent.
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Which of the following polynomial functions have exactly 5 roots, including all real and imaginary roots?Responsesf(x)=5x4+x3−x2+x−5𝑓(𝑥)=5𝑥4+𝑥3−𝑥2+𝑥−5f of x is equal to 5 x to the 4th power plus x cubed minus x squared plus x minus 5f(x)=4x5+3x4+2x3+x2+x𝑓(𝑥)=4𝑥5+3𝑥4+2𝑥3+𝑥2+𝑥f of x is equal to 4 x to the 5th power plus 3 x to the 4th power plus 2 x raised to the 3 power plus x squared plus xf(x)=5x6−5x4+5x2−5𝑓(𝑥)=5𝑥6−5𝑥4+5𝑥2−5f of x is equal to 5 x to the 6th power minus 5 x to the 4th power plus 5 x squared minus 5f(x)=4x4−3x3+2x2−1
Which of the following polynomial functions have exactly 5 roots, including all real and imaginary roots?Responsesf(x)=5x4+x3−x2+x−5𝑓(𝑥)=5𝑥4+𝑥3−𝑥2+𝑥−5f of x is equal to 5 x to the 4th power plus x cubed minus x squared plus x minus 5f(x)=4x5+3x4+2x3+x2+x𝑓(𝑥)=4𝑥5+3𝑥4+2𝑥3+𝑥2+𝑥f of x is equal to 4 x to the 5th power plus 3 x to the 4th power plus 2 x raised to the 3 power plus x squared plus xf(x)=5x6−5x4+5x2−5𝑓(𝑥)=5𝑥6−5𝑥4+5𝑥2−5f of x is equal to 5 x to the 6th power minus 5 x to the 4th power plus 5 x squared minus 5f(x)=4x4−3x3+2x2−1𝑓(𝑥)=4𝑥4−3𝑥3+2𝑥2−1f of x is equal to 4 x to the 4th power minus 3 x cubed plus 2 x squared minus 1Graphing Calculator
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