To create our polynomial we will use this form: Where "a" can be any non-zero real number we choose and the z's are our three zeros. This is why the problem says "Find a polynomial... " instead of "Find the polynomial... ". So now we have all three zeros: 0, i and -i. The multiplicity of zero 2 is 2. Since integers are real numbers, our polynomial Q will have 3 zeros since its degree is 3. Since what we have left is multiplication and since order doesn't matter when multiplying, I recommend that you start with multiplying the factors with the complex conjugate roots. Q has... (answered by josgarithmetic).
Try Numerade free for 7 days. These are the possible roots of the polynomial function. Find a polynomial with integer coefficients that satisfies the... Find a polynomial with integer coefficients that satisfies the given conditions. Sque dapibus efficitur laoreet. Q has degree 3 and zeros 4, 4i, and −4i. Found 2 solutions by Alan3354, jsmallt9: Answer by Alan3354(69216) (Show Source): You can put this solution on YOUR website! Fusce dui lecuoe vfacilisis. Fuoore vamet, consoet, Unlock full access to Course Hero. Not sure what the Q is about. The Fundamental Theorem of Algebra tells us that a polynomial with real coefficients and degree n, will have n zeros.
That is, f is equal to x, minus 0, multiplied by x, minus multiplied by x, plus it here. Explore over 16 million step-by-step answers from our librarySubscribe to view answer. Solved by verified expert. If we have a minus b into a plus b, then we can write x, square minus b, squared right. Asked by ProfessorButterfly6063. So in the lower case we can write here x, square minus i square. In this problem you have been given a complex zero: i. According to complex conjugate theorem, if a+ib is zero of a polynomial, then its conjugate a-ib is also a zero of that polynomial. Let a=1, So, the required polynomial is.
Since there are an infinite number of possible a's there are an infinite number of polynomials that will have our three zeros. In standard form this would be: 0 + i. Will also be a zero. That is plus 1 right here, given function that is x, cubed plus x. The standard form for complex numbers is: a + bi. Nam lacinia pulvinar tortor nec facilisis. Now, as we know, i square is equal to minus 1 power minus negative 1.
Enter your parent or guardian's email address: Already have an account? By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy. But we were only given two zeros. The complex conjugate of this would be. Pellentesque dapibus efficitu. The simplest choice for "a" is 1. If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.