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2.10 Summary (EMBFZ)

Zero product law: if \(a \times b = 0\), then \(a = 0\) and/or \(b=0\).

Quadratic formula: \(x = \dfrac{b \pm \sqrt{b^2  4ac}}{2a}\).

Discriminant: \(\Delta = b^2  4ac\).
Nature of roots Discriminant Roots are nonreal \(\Delta <0\) Roots are real and equal \(\Delta = 0\) Roots are real and unequal:
 Rational roots
 Irrational roots
\(\Delta > 0\)
 \(Δ =\) squared rational number
 \(Δ =\) not squared rational number
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