document.write( "Question 100208: Let α and β be the two roots of a quadratic equation ax^2 + 2b^x + c = 0, where a, b and c are constants.
\n" ); document.write( "Obtain the quadratic equation whose two roots are λ and δ such that λ = α^2 + β^2 and δ = α^2 - β^2.
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Algebra.Com's Answer #72973 by Nate(3500)\"\" \"About 
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α = (-2b + sqrt(4b^2 - 4ac))/2a and β = (-2b - sqrt(4b^2 - 4ac))/2a
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\n" ); document.write( "(x - λ)(x - δ) = 0
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\n" ); document.write( "(x - α^2 - β^2)(x - α^2 + β^2) = 0
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\n" ); document.write( "(x - ((-2b + sqrt(4b^2 - 4ac))/2a)^2 - ((-2b - sqrt(4b^2 - 4ac))/2a)^2)(x - α^2 + β^2) = 0
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\n" ); document.write( "(x - (-2b + sqrt(4b^2 - 4ac))^2/4a^2 - (-2b - sqrt(4b^2 - 4ac))^2/4a^2)(x - α^2 + β^2) = 0
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\n" ); document.write( "(x - (4b^2 - 4b*sqrt(4b^2 - 4ac) + 4b^2 - 4ac)/4a^2 - (4b^2 + 4b*sqrt(4b^2 - 4ac) + 4b^2 - 4ac)/4a^2)(x - α^2 + β^2) = 0
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\n" ); document.write( "(x - (8b^2 - 8b*sqrt(b^2 - ac) - 4ac)/4a^2 - (8b^2 + 8b*sqrt(b^2 - ac) - 4ac)/4a^2)(x - α^2 + β^2) = 0
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\n" ); document.write( "(x - (2b^2 - 2b*sqrt(b^2 - ac) - ac)/a^2 - (2b^2 + 2b*sqrt(b^2 - ac) - ac)/a^2)(x - α^2 + β^2) = 0
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\n" ); document.write( "(x + (-2b^2 + 2b*sqrt(b^2 - ac) + ac)/a^2 + (-2b^2 - 2b*sqrt(b^2 - ac) + ac)/a^2)(x - α^2 + β^2) = 0
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\n" ); document.write( "(x + (-4b^2 + 2ac)/a^2)(x - α^2 + β^2) = 0
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\n" ); document.write( "(x + (-4b^2 + 2ac)/a^2)(x - ((-2b + sqrt(4b^2 - 4ac))/2a)^2 + ((-2b - sqrt(4b^2 - 4ac))/2a)^2) = 0
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\n" ); document.write( "(x + (-4b^2 + 2ac)/a^2)(x - (2b^2 - 2b*sqrt(b^2 - ac) - ac)/a^2 + (2b^2 + 2b*sqrt(b^2 - ac) - ac)/a^2) = 0
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\n" ); document.write( "(x + (-4b^2 + 2ac)/a^2)(x + (-2b^2 + 2b*sqrt(b^2 - ac) + ac)/a^2 + (2b^2 + 2b*sqrt(b^2 - ac) - ac)/a^2) = 0
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\n" ); document.write( "(x + (-4b^2 + 2ac)/a^2)(x + 4b*sqrt(b^2 - ac)/a^2) = 0
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\n" ); document.write( "x^2 + x(-4b^2 + 2ac)/a^2 + x*4b*sqrt(b^2 - ac)/a^2 + (-4b^2 + 2ac)4b*sqrt(b^2 - ac)/a^4 = 0 \n" ); document.write( "
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