Form a quadratic polynomial with integer coefficients whose zeroes are $\frac{1}{2}$ and −4.

If α and β are zeros of $a{x}^2+bx+c$, then:

**α + β = −$b$/a** (sum of zeros).
**α · β = $c$/a** (product of zeros).

**Why**: $a{x}^2+bx+c=a(x$ − α)$(x$ − β) = $a$[$x^2$ − (α+β)$x$ + αβ].
Matching coefficients with $x^2+(b/a)x+(c/a)$: coefficient of $x$ → −(α+β) = $b$/a → α+β = −$b$/a, and constant: αβ = $c$/a.

**Reverse use**: To form a quadratic with given zeros α, β, write
$k$[$x^2$ − (α+β)$x$ + αβ]
for any non-zero constant $k$ (usually $k=1$).