Question

Suppose $a$ and $b$ are the solutions to the quadratic equation $2x^2-3x-6=0$. Find the value of $(a+2)(b+2)$.

Answer 1

we have that

2x²-3x-6=0
using a graph tool----------> to resolve the second order equation
see the attached figure
the solution is
x=-1.137
x=2.637

therefore
a=-1.137
b=2.637
so
(a+2)*(b+2)-----------> (-1.137+2)*(2.637+2)--------> 0.863*4.637---> 4

the answer is 4