The Nature of the Roots (Grade 12 NSC Matric Mathematics): Quizzes

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The Nature of the Roots
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What is the discriminant of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0?

b2−4acb^2 - 4ac

What do the roots of a quadratic equation represent on a graph?

The x-intercepts of the parabola

What is the nature of the roots when Δ<0\Delta < 0?

Non-real or complex roots

How does the parabola behave when Δ<0\Delta < 0?

Does not intersect the x-axis

What is the nature of the roots when Δ=0\Delta = 0?

One real, equal, and rational root

How does the parabola behave when Δ=0\Delta = 0?

Touches x-axis at exactly one point

What is the nature of roots when Δ=25\Delta = 25 (a perfect square)?

Real, rational, and unequal

What is the nature of roots when Δ=24\Delta = 24 (not a perfect square)?

Real, irrational, and unequal

What condition must be met for a quadratic equation to have equal roots?

Set Δ=0\Delta = 0

In geometry problems, why are negative solutions typically rejected?

Measurements must be positive values

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