Answer:
The two values of x that are roots are:
[tex]x_{1} = \frac{-3 + \sqrt{21} }{2}[/tex]
[tex]x_{2} = \frac{-3 - \sqrt{21} }{2}[/tex]
Step-by-step explanation:
A cuadratic function has the form [tex]ax^{2} + bx +c = 0[/tex]
To calculate the roots of the cuadratic equation [tex]x^{2} + 3x -3 = 0[/tex] you have to solve the formula:
[tex]x = \frac{-b}{2a}[/tex] ±[tex]\frac{\sqrt{b^{2} -4ac} }{2a}[/tex]
In this case, a =1, b=3 and c= -3
Replacing the values of a,b and c in the formula:
[tex]x = \frac{-3}{(2)(1)}[/tex] ± [tex]\frac{\sqrt{(3)^{2} - (4)(1)(-3) } }{(2)(1)}[/tex]
Solving the mathematic operations:
x = [tex]\frac{-3}{2}[/tex] ± [tex]\frac{\sqrt{9 + 12 } }{2}[/tex]
The two roots are:
[tex]x_{1} = \frac{-3 + \sqrt{21} }{2}[/tex]
[tex]x_{2} = \frac{-3 - \sqrt{21} }{2}[/tex]
