Answer:
[tex]A) \ \{ \dfrac{-3 + \sqrt{29} }{2}, \dfrac{-3 - \sqrt{29} }{2} \}[/tex]
Step-by-step explanation:
The quadratic equation to be solved is presented here as follows;
x² + 3·x - 5 = 0
The quadratic formula for a quadratic equation of the form, a·x²+b·x + c = 0, where 'a', 'b', and 'c' are constants and 'x' is unknown, is given as follows;
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4 \cdot a \cdot c} }{2 \cdot a}[/tex]
By comparison with the given equation, we have;
a = 1, b = 3, and c = -5
By plugging in the values, we get;
[tex]x = \dfrac{-3 \pm \sqrt{3^2 - 4 \times 1 \times (-5)} }{2 \times 1}[/tex]
Therefore;
[tex]x = \{\dfrac{-3 + \sqrt{9 + 20} }{2}, \dfrac{-3 - \sqrt{9 + 20} }{2}\} = \{\dfrac{-3 + \sqrt{29} }{2}, \dfrac{-3 - \sqrt{29} }{2}\}[/tex]
[tex]x= \{\dfrac{-3 + \sqrt{29} }{2}, \dfrac{-3 - \sqrt{29} }{2}\}[/tex]
