The sum the zeros keep

x² − 5x + 6 has zeros 2 and 3. Their sum is 5. In ax² + bx + c, a is the number before x², so a = 1. The letter b is the number before x, so b = −5. Then −b/a = −(−5)/1 = 5. The same.

The rule

If `ax² + bx + c` has zeros, their sum is `−b/a`.

Here a, b and c are the coefficients. The a is in front of x². The b is in front of x. The c stands alone.

Add the zeros first. Then read a and b from the quadratic. The sum and −b/a agree whenever the quadratic has zeros. A touching curve has one zero. That zero counts twice.

The curve of x² − 6x + 9 touches the axis once, at 3. Count that zero twice: 3 + 3 = 6.

Look at the last row. Here a = −5 and b = 40. So −b/a = −40/(−5) = 8, which is the sum.

Try the lab to finish this lesson.