Q. If the factors of the quadratic function (g) are (x – 7) and (x + 3), what are the zeros of function (g)?

Step 1 — Definition of a zero. A zero of the function g is any real number x for which g(x) = 0.

Step 2 — Express g(x) using its factors. If the given factors of g are (x − 7) and (x + 3), then g(x) has the form \(g(x)=k(x-7)(x+3)\) for some constant \(k\neq 0\). The constant factor \(k\) does not affect the zeros.

Step 3 — Set the function equal to zero and apply the zero-product property. To find zeros we solve \(g(x)=0\), which gives

\((x-7)(x+3)=0\)

The zero-product property states that if a product of two factors equals zero, then at least one of the factors must be zero. Thus we solve the two simple equations separately:

1. Solve \(x-7=0\), which yields \(x=7\).
2. Solve \(x+3=0\), which yields \(x=-3\).

Step 4 — Verify by substitution (optional check).

• For \(x=7\): \((7-7)(7+3)=0\cdot 10=0\).
• For \(x=-3\): \((-3-7)(-3+3)=(-10)\cdot 0=0\).

Conclusion. The zeros of g are \(x=7\) and \(x=-3\).