Answer :
The roots of the equation is x = 4.56 OR x = 0.44
Quadratic equation
From the question, we are to determine the roots of the given equation
The given equation is
x² -5x +2 = 0
Using the formula method,
[tex]x =\frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]
In the given equation,
a = 1, b = -5, c = 2
Putting the values into the formula,
[tex]x =\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(2) } }{2(1)}[/tex]
[tex]x =\frac{5 \pm \sqrt{25-8} }{2}[/tex]
[tex]x =\frac{5 \pm \sqrt{17} }{2}[/tex]
[tex]x =\frac{5 + \sqrt{17} }{2}[/tex] OR [tex]x =\frac{5 - \sqrt{17} }{2}[/tex]
[tex]x =\frac{5 + 4.12}{2}[/tex] OR [tex]x =\frac{5 - 4.12}{2}[/tex]
[tex]x =\frac{9.12}{2}[/tex] OR [tex]x =\frac{0.88}{2}[/tex]
x = 4.56 OR x = 0.44
Hence, the roots of the equation is x = 4.56 OR x = 0.44
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