The two values of x that are roots of this equation x²-5x+3=0 are x = [tex]\frac{5+\sqrt{13} }{2}[/tex]and x = [tex]\frac{5-\sqrt{13} }{2}[/tex]. This can be obtained by using formula to find roots of quadratic equation.
What is the formula to find roots of quadratic equation?
For a quadratic equation ax²+bx+c = 0,
the roots are obtained using the formula, [tex]x =\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] and
[tex]x =\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
Find the two values of x:
Given that the quadratic equation is x²-5x+3=0
⇒a = 1, b= - 5, c = 3
By using the formula to find roots of quadratic equation the roots are,
[tex]x =\frac{-(-5)+\sqrt{(-5)^{2}-4(1)(3) } }{2(1)}[/tex] and [tex]x =\frac{-(-5)-\sqrt{(-5)^{2}-4(1)(3) } }{2(1)}[/tex]
[tex]x =\frac{5+\sqrt{25-12 } }{2}[/tex] and [tex]x =\frac{5-\sqrt{25-12 } }{2}[/tex]
[tex]x =\frac{5+\sqrt{13 } }{2}[/tex] and [tex]x =\frac{5-\sqrt{13 } }{2}[/tex]
These are the required roots.
Hence the two values of x that are roots of this equation x²-5x+3=0 are x = [tex]\frac{5+\sqrt{13} }{2}[/tex]and x = [tex]\frac{5-\sqrt{13} }{2}[/tex].
Therefore the correct answer is option A. and option D.
Learn more about solving quadratic equations here:
brainly.com/question/1214333
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