A quadratic equation, whose roots are 2 + √3 and 2 – √3 = ……………….
A quadratic equation, whose roots are 2 + √3 and 2 – √3 = ……………….
A) x2 – x – 4 = 0
B) x2 – 4x + 1 = 0
C) x2 + 4x + 3 = 0
D) x2 + x – 3 = 0
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Correct option is (B) x2 – 4x + 1 = 0
Roots of quadratic equation are \(2+\sqrt{3}\) and \(2-\sqrt{3}.\)
\(\therefore\) Required quadratic equation is
\((x-(2+\sqrt{3}))(x-(2-\sqrt{3}))=0\)
\(\Rightarrow((x-2)-\sqrt3)((x-2)+\sqrt3)=0\)
\(\Rightarrow(x-2)^2-(\sqrt3)^2=0\) \((\because(a-b)(a+b)=a^2-b^2)\)
\(\Rightarrow x^2-4x+4-3=0\) \((\because(a-b)^2=a^2-2ab+b^2)\)
\(\Rightarrow x^2-4x+1=0\)
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