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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 rootsDiscriminant
    Roots are non-real\(\Delta <0\)
    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