The solution of quadratic equation [tex]3 x^{2}-5 x-2=0[/tex] is [tex]x=2 \text { or } \frac{-1}{3}[/tex]
Solution:
Given, equation is [tex]3 x^{2}-5 x-2=0[/tex]
We have to solve the above given quadratic equation.
Now, take the given quadratic equation
[tex]\rightarrow 3 x^{2}-5 x-2=0[/tex]
Splitting “-5x” as -6x + x
[tex]\rightarrow 3 x^{2}-6 x+x-2=0[/tex]
Take “3x” as common term from first two terms
[tex]\rightarrow 3 x(x-2)+1(x-2)=0[/tex]
Take (x - 2) as common
[tex]\rightarrow(x-2)(3 x+1)=0[/tex]
Equating to zero we get,
[tex]\begin{array}{l}{\rightarrow x-2=0 \text { or } 3 x+1=0} \\\\ {\rightarrow x=2 \text { or } 3 x=-1} \\\\ {\rightarrow x=2 \text { or } x=\frac{-1}{3}} \\\\ {\rightarrow x=2 \text { or } \frac{-1}{3}}\end{array}[/tex]
Hence, the roots the quadratic equation are 2 and [tex]\frac{-1}{3}[/tex]
