Question

X2 - 4x + 1 = 0 find its roots

Answer 1

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• x² - 4x + 1 = 0
• a = 1
• b = - 4
• c = 1

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• Zeros of the quadratic equation is the value of the variable for which when replaced in the quadratic equations the value for the quadratic equation changes to zero.

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• ax² + bx + c = 0

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• Find the roots/zeros of the given equation.

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• x² - 4x + 1 = 0
• Quadratic formula = $\bold{\frac{-b\: \pm\:{\sqrt{b^{2}\:-\:4ac} }}{2a}}$  

• α =  $\bold{\frac{4\: \pm\:{\sqrt{-4^{2}\:-\:4(1)(1)} }}{2(1)}}$  

• α =  $\bold{\frac{4\: \pm\:{\sqrt{16\:-\:4} }}{2}}$

• α = $\bold{\frac{4\: \pm\:{\sqrt{12} }}{2}}$  

• α = $\bold{\frac{4\: \pm\:2{\sqrt{3} }}{2}}$

• α =  $\bold{2\: +\:{\sqrt{3} }}$

• β = $\bold{2\: -\:{\sqrt{3} }}$