If α, β be the roots of the quadratic equation x^2 – 2x + 1 = 0, then the quadratic equation whose roots are α + β and αβ is ………………
If α, β be the roots of the quadratic equation x2 – 2x + 1 = 0, then the quadratic equation whose roots are α + β and αβ is ………………
A) x2 – 2x – 1 = 0
B) x2 + 2x + 1 = 0
C) x2 + 2x -1 = 0
D) x2 – 3x + 2 = 0
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Correct option is (D) \(x^2-3x+2=0\)
Given that \(\alpha\;and\;\beta\) are the roots of the quadratic equation \(x^2-2x+1=0.\)
\(\Rightarrow(x-1)^2=0\)
\(\Rightarrow\) x = 1, 1
\(\therefore\alpha=1,\beta=1\)
\(\therefore\alpha+\beta=1+1=2\)
& \(\alpha\beta=1.1=1\)
\(\therefore\) Required quadratic equation is
\(x^2-\) (Sum of roots)x + Product of roots = 0
\(\Rightarrow x^2-(\alpha+\beta+\alpha\beta)x+(\alpha+\beta)\,\alpha\beta=0\)
\(\Rightarrow x^2-(2+1)x+2.1=0\)
\(\Rightarrow x^2-3x+2=0\)
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