If one root of the quadratic equation x^2 – 4x + 1 = 0 is 2 + √3, then the other root is …………
If one root of the quadratic equation x2 – 4x + 1 = 0 is 2 + √3, then the other root is …………
A) 7 + √3
B) 7 – 4√3
C) 1 + √3
D) 2 – √3
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Correct option is (D) 2 – √3
Given quadratic equation is \(x^2-4x+1=0\)
Let the other root be x.
\(\therefore\) Sum of roots \(=\frac{-(-4)}1=4\)
\(\Rightarrow\) \(x+2+\sqrt{3}=4\)
\(\Rightarrow\) \(x=4-2-\sqrt3\)
\(\Rightarrow\) x = \(2-\sqrt{3}\)
Hence, the other root is \(2-\sqrt{3}.\)
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