So x = 2 + or 2 – . “Product” means to multiply, so use FOIL to multiply (2 + ) × (2 − ) to
get 4 – 2 + 2 − ( )^2 = 4 – 2 = 2, which is (B).
Wow, that was a lot of work! Wouldn’t it be great if there were a shortcut? Actually, there is! When a
quadratic is in the form y = ax^2 + bx + c, the product of the roots is equal to the value of c divided by the
value of a. In this case, that’s 6 ÷ 3 = 2! It’s the same answer for a lot less work. (See the inset “The Root
of the Problems” for this and another handy trick—they’re worth memorizing.)
The Root of the Problems
Sometimes you’ll be asked to solve for the sum or the product of the roots of a quadratic equation.
You can use the quadratic formula and then add or multiply the results, but it’s quicker to just
memorize these two expressions.sum of the roots: –product of the roots: IMAGINARY AND COMPLEX NUMBERS
So far you have been working with real numbers, which are any numbers that you can place on a number
line. The SAT will also ask you to do mathematical operations with imaginary or complex numbers.