Answer:
The two roots are;
[tex]x=-2,x=-\frac{3}{2}[/tex]
Step-by-step explanation:
The given polynomial is;
[tex]2x^2+7x+6[/tex]
To find the roots of this polynomial; we set the function to zero
[tex]2x^2+7x+6=0[/tex]
We split the middle term to obtain;
[tex]2x^2+4x+3x+6=0[/tex]
Factor by grouping;
[tex]2x(x+2)+3(x+2)=0[/tex]
[tex](x+2)(2x+3)=0[/tex]
Use the zero product property;
[tex](x+2)=0,(2x+3)=0[/tex]
The two roots are;
[tex]x=-2,x=-\frac{3}{2}[/tex]
