Step-by-step explanation: If a polynomial has degree n and are zeroes of the polynomial, then the polynomial is defined as. So now we have all three zeros: 0, i and -i. Explore over 16 million step-by-step answers from our librarySubscribe to view answer. Q has... (answered by Boreal, Edwin McCravy). This is our polynomial right. Not sure what the Q is about. I, that is the conjugate or i now write. If we have a minus b into a plus b, then we can write x, square minus b, squared right. 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. Find a polynomial with integer coefficients that satisfies the given conditions Q has degree 3 and zeros 3, 3i, and _3i. That is, f is equal to x, minus 0, multiplied by x, minus multiplied by x, plus it here.
Answered step-by-step. Since 3-3i is zero, therefore 3+3i is also a zero. Asked by ProfessorButterfly6063. Q has degree 3 and zeros 4, 4i, and −4i. These are the possible roots of the polynomial function. It is given that the polynomial R has degree 4 and zeros 3 − 3i and 2. Create an account to get free access. The multiplicity of zero 2 is 2. Will also be a zero. The other root is x, is equal to y, so the third root must be x is equal to minus. The standard form for complex numbers is: a + bi. Another property of polynomials with real coefficients is that if a zero is complex, then that zero's complex conjugate will also be a zero.
Find a polynomial with integer coefficients and a leading coefficient of one that... (answered by edjones). Fusce dui lecuoe vfacilisis. Q has... (answered by tommyt3rd). Q has... (answered by josgarithmetic). Find a polynomial with integer coefficients that satisfies the given conditions. The Fundamental Theorem of Algebra tells us that a polynomial with real coefficients and degree n, will have n zeros. We have x minus 0, so we can write simply x and this x minus i x, plus i that is as it is now. This is why the problem says "Find a polynomial... " instead of "Find the polynomial... ". By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy. Using this for "a" and substituting our zeros in we get: Now we simplify. The complex conjugate of this would be. Q(X)... (answered by edjones).
Q has... (answered by CubeyThePenguin). In standard form this would be: 0 + i. Fuoore vamet, consoet, Unlock full access to Course Hero. Since there are an infinite number of possible a's there are an infinite number of polynomials that will have our three zeros.
S ante, dapibus a. acinia. Now, as we know, i square is equal to minus 1 power minus negative 1. Nam lacinia pulvinar tortor nec facilisis. Solved by verified expert.
Try Numerade free for 7 days. This problem has been solved! 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. Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website! Since this simplifies: Multiplying by the x: This is "a" polynomial with integer coefficients with the given zeros. 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. Since we want Q to have integer coefficients then we should choose a non-zero integer for "a". We will need all three to get an answer.
Answered by ishagarg. Pellentesque dapibus efficitu. Let a=1, So, the required polynomial is. In this problem you have been given a complex zero: i. But we were only given two zeros. Find a polynomial with integer coefficients that satisfies the... Find a polynomial with integer coefficients that satisfies the given conditions. For given degrees, 3 first root is x is equal to 0. Complex solutions occur in conjugate pairs, so -i is also a solution.