Find the roots of quadratic equations x2 - 4x + 1 = 0 – InterviewSolution

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Find the roots of quadratic equations x2 - 4x + 1 = 0

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x² - 4x + 1 = 0

⇒ x² - 4x = -1

⇒ x² - 2 \(\times\)x \(\times\)2 + 2² = - 1 + 2² (Adding 2² on both sides)

⇒ (x - 2)² = - 1 + 4 = 3

⇒ x - 2 = ±√3

⇒ x - 2 = √3 or x - 2 = - √3

⇒ x = 2 + √3 or x = 2 -√3

Hence, 2 + √3 and 2 - √3 are the roots of the given equation.

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