Find the discriminant of $3x^2-7x+2=0$.

Rewrite $a{x}^2+bx+c=0$ as a product $(px+q)(rx+s)=0$, then use the **zero-product property**: a product is zero iff one of its factors is zero.

**Steps for $x^2+bx+c=0\ast \ast (a=1)$:
1. Find two numbers that MULTIPLY to $c$ and ADD to $b$.
2. Use them as the constants in $(x+p)(x+q)$.

**Example**: $x^2-7x+12=0$ → product 12, sum −7 → numbers −3 and −4 → $(x-3)(x-4)=0$ → $x=3$ or 4.

**For $a{x}^2+bx+c$ with a ≠ 1**: split the middle term — find two numbers multiplying to $a\times c$ and summing to $b$. Then group.

Example: $2x^2+7x+3=0.a\times c=6$, sum = 7 → 6 and 1. Split: $2x^2+6x+x+3=2x(x+3)+1(x+3)=(2x+1)(x+3)=0$ → $x=-1/2$ or −3.