ax² + bx + c = 0; roots use the discriminant b² − 4ac.
Find real or complex roots and explore a parabola — the roots and the vertex are marked on the graph, the discriminant verdict is spelled out in words, and the factorised form is shown whenever the roots are tidy numbers.
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Find real or complex roots and explore a parabola — the roots and the vertex are marked on the graph, the discriminant verdict is spelled out in words, and the factorised form is shown whenever the roots are tidy numbers.
For x² − 3x + 2 = 0, the roots are 1 and 2 and the discriminant is 1, so the equation factorises as (x − 1)(x − 2) = 0; both roots and the vertex at (1.5, −0.25) are marked on the graph. For x² + 1 = 0 the discriminant is −4, so there are no real roots — only the complex pair i and −i.
ax² + bx + c = 0; roots use the discriminant b² − 4ac.
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