Let [tex]x_1 , x_2[/tex] be the roots of the equation [tex]3x^2-5x-7[/tex]. By the Viet theorem you have that [tex] \left \{ {{x_1+x_2=- \frac{5}{3} } \atop {x_1x_2= \frac{-7}{3} }} \right. [/tex].
For the equation [tex]x^2+bx+c = 0[/tex] you'll have that [tex]c=(x_1+2)(x_2+2)=x_1x_2+2(x_1+x_2)+4=\frac{-7}{3}+2\cdot(- \frac{5}{3} )+4[/tex]
That is [tex]\frac{-7}{3}- \frac{10}{3} +4=- \frac{5}{3} [/tex].
Answer: [tex]- \frac{5}{3} [/tex]
