When we expand this expression, we'll have a quadratic equation in the general form.
The general form of quadratic equations looks like this :
[tex]a{ x }^{ 2 }+bx+c\quad =\quad 0[/tex]
( a is coefficent of [tex] x^{2} [/tex] , b is coefficient of x and c is the constant)
So let's expand the expression.
[tex](2x+1)\cdot (x-2)\quad =\quad 0\\ \\ (2x\cdot x)+(2x\cdot -2)+(1\cdot x)+(1\cdot -2)\quad =\quad 0\\ \\ 2{ x }^{ 2 }+(-4x)+x-2\quad =\quad 0\\ \\ 2{ x }^{ 2 }-4x+x-2\quad =\quad 0\\ \\ 2{ x }^{ 2 }-3x-2\quad =\quad 0[/tex]
This how the final form of our equation :
[tex]\boxed { 2{ x }^{ 2 }-3x-2\quad =\quad 0 } [/tex]
As you can see [tex] x^{2} [/tex] 's coefficient (a) is 2 , x's coefficient (b) is -3 and the constant (c) is -2
[tex]\boxed { a=2,\quad b=-3,\quad c=-2 } [/tex]
