Given:
A quadratic equation is:
[tex]3x^2+9x-2=0[/tex]Find-:
The roots of the quadratic equation
Explanation-:
Use quadratic formula:
[tex]ax^2+bx+c=0[/tex]Roots of the equation,
[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]The roots of the given equation are:
[tex]3x^2+9x-2=0[/tex][tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x_{1,2}=\frac{-9\pm\sqrt{9^2-4(3)(-2)}}{2(3)} \\ \\ x_{1,2}=\frac{-9\pm\sqrt{81-(-24)}}{6} \\ \\ x_{1,2}=\frac{-9\pm\sqrt{81+24}}{6} \\ \\ x_{1,2}=\frac{-9\pm\sqrt{105}}{6} \end{gathered}[/tex]The roots of a quadratic equation are:
[tex]\begin{gathered} x_{1,2}=\frac{-9\pm\sqrt{105}}{6} \\ \\ x_1=\frac{-9+\sqrt{105}}{6},x_2=\frac{-9-\sqrt{105}}{6} \end{gathered}[/tex][tex]\begin{gathered} x_1=\frac{-9+\sqrt{105}}{6},x_2=\frac{-9-\sqrt{105}}{6} \\ \\ x_1=0.2078,x_2=-3.2078 \end{gathered}[/tex]The roots of a quadratic equation are 0.2078 and -3.2078.
