document.write( "Question 362458: Suppose that a polynomial function of degree 5 with rational coefficients has -2-3i, -5 and square root of 7 as zeros. Find the other zeros.\r
\n" ); document.write( "\n" ); document.write( "a. 5, 2+3i
\n" ); document.write( "b. -2+3i, -square root of 7
\n" ); document.write( "c. 3i, -2
\n" ); document.write( "d. 5, -2+3i, square root of 7
\n" ); document.write( "e. none of the above
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Algebra.Com's Answer #258378 by CharlesG2(834)\"\" \"About 
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Suppose that a polynomial function of degree 5 with rational coefficients has -2-3i, -5 and square root of 7 as zeros. Find the other zeros.\r
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\n" ); document.write( "\n" ); document.write( "a. 5, 2+3i
\n" ); document.write( "b. -2+3i, -square root of 7
\n" ); document.write( "c. 3i, -2
\n" ); document.write( "d. 5, -2+3i, square root of 7
\n" ); document.write( "e. none of the above\r
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\n" ); document.write( "\n" ); document.write( "x + 2 - 3i = 0, x = -2 + 3i ->this should be a zero if we want i's to cancel out
\n" ); document.write( "x + 2 + 3i = 0, x = -2 - 3i ->know this is x is a zero
\n" ); document.write( "(x + 2 + 3i)(x + 2 - 3i) = x^2 + 2x - 3ix + 2x + 4 - 6i + 3ix + 6i - 9i^2
\n" ); document.write( "= x^2 + 2x + 2x - 3ix + 3ix - 6i + 6i + 4 + 9 = x^2 + 4x + 13
\n" ); document.write( "this leaves us with answers:
\n" ); document.write( "b. -2+3i, -square root of 7
\n" ); document.write( "d. 5, -2+3i, square root of 7
\n" ); document.write( "AND e. none of the above\r
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\n" ); document.write( "\n" ); document.write( "were told -2-3i, -5 and square root of 7 are zeros
\n" ); document.write( "there should be 5 zeros
\n" ); document.write( "so answers are either b. -2+3i, -square root of 7
\n" ); document.write( "OR e. none of the above\r
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\n" ); document.write( "\n" ); document.write( "(x + sqrt(7))(x - sqrt(7)) = x^2 - 7, square roots canceled out\r
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\n" ); document.write( "\n" ); document.write( "so if we want i's to cancel out and square roots of 7 to cancel out
\n" ); document.write( "then
\n" ); document.write( "-2 - 3i, -5, square root of 7, -2 + 3i, and -square root of 7 are the roots
\n" ); document.write( "to get all rational coeffiecients
\n" ); document.write( "so answer is b. -2+3i, -square root of 7\r
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\n" ); document.write( "\n" ); document.write( "and 5th degree polynomial is:
\n" ); document.write( "-2 - 3i, -2 + 3i, sqrt(7), -sqrt(7), -5 roots of 5th degree polynomial
\n" ); document.write( "(x + 2 + 3i)(x + 2 - 3i)(x - sqrt(7))(x + sqrt(7))(x + 5) = 0
\n" ); document.write( "(x^2 + 4x + 13)(x^2 - 7)(x + 5) = 0
\n" ); document.write( "(x^4 - 7x^2 + 4x^3 - 28x + 13x^2 - 91)(x + 5) = 0
\n" ); document.write( "(x^4 + 4x^3 + 6x^2 - 28x - 91)(x + 5) = 0
\n" ); document.write( "x^5 + 4x^4 + 6x^3 - 28x^2 - 91x + 5x^4 + 20x^3 + 30x^2 - 140x - 455 = 0
\n" ); document.write( "x^5 + 9x^4 + 26x^3 + 2x^2 - 231x - 455 = 0\r
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