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DEMO: The discriminant

Worked examples

• $x^2 - 6x + 5$: $b^2 - 4ac = 36 - 20 = 16$.
• $x^2 + x + 1$: $1 - 4 = -3 < 0$, so no real roots.
• $x^2 - 2x + 1$: $4 - 4 = 0$, so one repeated root.

Key points

• The discriminant is $b^2 - 4ac$.
• Here $a = 1$, $b = -4$, $c = 4$.
• Work out $b^2 - 4ac$ and check its sign.
• $3^2 - 4(2)(5) = 9 - 40$.
• Work out $b^2 - 4ac$ and check its sign.
• $(-5)^2 - 4(1)(6) = 25 - 24$.

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