Problem

Factor \(4x^{2}+20x+25=0\) by identifying the square bases whose double product is \(20x\). Solve the repeated linear factor and report the zero and its multiplicity.

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Roots 2x and 5; middle check −2(2x)(5) = −20x; squared factor (2x − 5)² = 0; repeated zero x = 5/2; multiplicity 2; expansion 4x² − 20x + 25.

end roots=a=2x,b=5; middle check=2ab=20x; squared factor=(2x+5)²=0; repeated zero=5; multiplicity2; graph meaning=tangent at the copied value

end roots=a=2x,b=5; middle check=2ab=20x; factored=(2x+5)²=0; repeated zero=x=-5/2; multiplicity=2; graph meaning=tangent x-intercept(-5/2,0)

end roots=a=2x,b=5; middle check=2ab=20x; squared factor=(2x+5)²=0; zeros=-5/2 and -5/2; multiplicity=1 each; graph meaning=two distinct x-intercepts

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