The two values of x that are roots to the given equation are [tex]x= -1 + \sqrt{6}[/tex] and [tex]x= -1 - \sqrt{6}[/tex]
From the question,
We are to determine the values of x that are roots to the quadratic equation x² +2x -5=0
Using the quadratic formula
[tex]x= \frac{-b \pm \sqrt{b^{2} -4ac} }{2a}[/tex]
From the given equation x² +2x -5=0
[tex]a = 1, \ b = 2, \ and \ c=-5[/tex]
Putting the values into the equation, we get
[tex]x= \frac{-(2) \pm \sqrt{(2)^{2} -4(1)(-5)} }{2(1)}[/tex]
This becomes
[tex]x= \frac{-2 \pm \sqrt{4 --20} }{2}[/tex]
[tex]x= \frac{-2 \pm \sqrt{4+20} }{2}[/tex]
[tex]x= \frac{-2 \pm \sqrt{24} }{2}[/tex]
Then,
[tex]x= \frac{-2 \pm 2\sqrt{6} }{2}[/tex]
∴ [tex]x= -1 \pm \sqrt{6}[/tex]
[tex]x= -1 + \sqrt{6} \ OR \ x= -1 - \sqrt{6}[/tex]
Hence, the two values of x that are roots to the given equation are [tex]x= -1 + \sqrt{6}[/tex] and [tex]x= -1 - \sqrt{6}[/tex]
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