Question

f(x)=ˣ⁴+10ˣ³−15ˣ²−40x+44 What are the real zeros? Select the correct choice below and, if necessary, fill in the answer box to complete your answer. A. x= (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression. Use a comma to separate answers as needed.) B. There are no real zeros. Use the real zeros to factor f. f(x)= (Simplify your answer. Type your answer in factored form. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression.)

Answer 1

Finding the real zeros of f(x)=x⁴+10x³−15x²−40x+44 involves methods like factoring, synthetic division, the Rational Root Theorem, or numerical approximation through the use of technology.

Step-by-step explanation:

The function f(x) = x⁴ + 10x³ - 15x² - 40x + 44 is a polynomial equation, and the task is to find its real zeros. The real zeros of a polynomial equation are the values of x for which f(x) is equal to zero. In order to find these zeros, one could use several methods such as factoring, synthetic division, or the Rational Root Theorem. However, without a given way to simplify this high-degree polynomial or any special pattern, numeric methods or technology like graphing calculators or computer algebra systems are often used to approximate the zeros. Once the real zeros are found, we can then factor the polynomial using those zeros. If we are unable to determine the exact real zeros analytically, we might state B, 'There are no real zeros'.