Answer:[tex]6x^{2}-13x-5[/tex]
Step-by-step explanation:
Given that the two roots of the quadratic equation are [tex]\frac{-1}{3}[/tex] and [tex]\frac{5}{2}[/tex].
If [tex]\alpha[/tex][tex],\beta[/tex] are the roots of the quadratic equation,the equation is [tex](x-\alpha )(x-\beta )[/tex].
It is given that [tex]\alpha =\frac{-1}{3}[/tex] and [tex]\beta =\frac{5}{2}[/tex].
So,the equation is
[tex](x-(\frac{-1}{3}))(x-\frac{5}{2})[/tex]
=[tex]x^{2}-\frac{5}{2}x+\frac{x}{3}-\frac{5}{6}[/tex]
=[tex]6x^{2}-13x-5[/tex]
