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Which of the following are solutions to the equation below?Check all that apply.x-5x+ 1 = 0A. x =5+29B. x = 5 - 292.C. x= 5+ V212D. x= -1 - 212E. x = =*+,x21F. x =5 - 2152



Answer :

[tex]\begin{gathered} x\text{ = }\frac{5+\sqrt[]{21}}{2} \\ x\text{ = }\frac{5-\sqrt[]{21}}{2} \end{gathered}[/tex]

It is calculated using the quadratic formula

[tex]x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

In the equation

[tex]x^2-5x+1=0[/tex]

a = 1, b = -5 and c = 1

Substitute the given to the quadratic formula

[tex]\begin{gathered} x\text{ = }\frac{5+\sqrt[]{21}}{2} \\ x\text{ = }\frac{5-\sqrt[]{21}}{2} \end{gathered}[/tex]

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