If α, β be the roots of the quadratic equation x2 – 2x + 1 = 0, th

1.	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
Answer» 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 \(\Rightarrow x^2-(\alpha+\beta+\alpha\beta)x+(\alpha+\beta)\,\alpha\beta=0\) \(\Rightarrow x^2-(2+1)x+2.1=0\) \(\Rightarrow x^2-3x+2=0\) Correct option is D) x² – 3x + 2 = 0

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

Answer»

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

\(\Rightarrow x^2-(\alpha+\beta+\alpha\beta)x+(\alpha+\beta)\,\alpha\beta=0\)

\(\Rightarrow x^2-(2+1)x+2.1=0\)

\(\Rightarrow x^2-3x+2=0\)

Correct option is D) x² – 3x + 2 = 0