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

Question

Please explain and help. Thank you in advance

Answer 1

Using Vieta's formulas, we have:

$$ \begin{eqnarray} a+b &=& -\frac{-3}{2} = \frac{3}{2}\\ ab &=& \frac{-6}{2} = -3 \end{eqnarray} $$

So:

$$ \begin{eqnarray} (a+2)(b+2) &=& ab + 2a + 2b + 4\\ &=& ab + 2(a+b) + 4\\ &=& -3 + 2(\frac{3}{2}) + 4\\ &=& 4 \end{eqnarray} $$