To determine A polynomial function of lowest degree with the rational coefficients that has the given numbers as some of its zeros. Explanation Definition used: “If a + c b and a − c b , where a, b and c are rational and b is not perfect square, is a zero of a polynomial function f ( x ) with rational coefficients then its conjugate a − c b is also a zero If a complex number a + b i , b ≠ 0 , is a zero of a polynomial function f ( x ) with real coefficients then its conjugate a − b i is also a zero Every polynomial function f of degree, n, with n ≥ 1 , can be factored into n linear factors that is, f ( x ) = a n ( x − c 1 ) ( x − c 2 ) ⋯ ( x − c n ) ” Calculation: Obtain the polynomial function of lowest degree as follows. The given zeros are 2 − i , − 1 . From the definition used, as the coefficients are rational, the irrational zeros always occurs in pair. Then, the conjugate of 2 − i that is 2 + i is also a zero. Thus, the zeros are 2 − i , − 1 , 2 + i . Form the linear factors with the zeros 2 − i , − 1 , 2 + i that is, x − ( 2 − i ) , x + 1 and x − ( 2 + i ) . Here, the number can assume any nonzero number but to obtain the simplest polynomial let, a n = 1

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Chapter 4.4, Problem 34E

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A polynomial function of lowest degree with the rational coefficients that has the given numbers as some of its zeros.

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Chapter 4.4, Problem 33E

Chapter 4.4, Problem 35E

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5) You are purchasing a game for $30. You have a 5% off coupon and sales tax is 5%. What will your final price be? Does it matter if you take off the coupon first or add in the tax first? 6) You have ten coupons that allow you to take 10% off the sales price of a jacket, and for some strange reason, the store is going to allow you to use all ten coupons! Does this mean you get the jacket for free? Let's really think about what would happen at the checkout. First, the teller would scan the price tag on the jacket, and the computer would show the price is $100. After the teller scans the first coupon, the computer will take 10% off of $100, and show the price is $90. (Right? Think about why this is.) Then after the teller scans the second coupon, the computer will take 10% off of $90. (a) Continue this reasoning to fill in the table below showing the price of the jacket (y) after you apply x coupons. (b) Make a graph showing the price of the jacket from x = 0 to x = 10 coupons applied.…

(a) (b) (c) (d) de unique? Answer the following questions related to the linear system x + y + z = 2 x-y+z=0 2x + y 2 3 rewrite the linear system into the matrix-vector form A = 5 Fuse elementary row operation to solve this linear system. Is the solution use elementary row operation to find the inverse of A and then solve the linear system. Verify the solution is the same as (b). give the null space of matrix A and find the dimension of null space. give the column space of matrix A and find the dimension of the column space of A (Hint: use Rank-Nullity Theorem).

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EBK ALGEBRA AND TRIGONOMETRY

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 6E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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