Last updated on Oct 23, 2026

Forming Quadratic Equations (Leaving Cert Mathematics): Quizzes

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Forming Quadratic Equations

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If the roots of a quadratic are $a$ and $b$ , which equation is formed?

$(x - a)(x - b) = 0$

When forming factors from roots, what must you do to each root?

Change the sign of each root

What is the first step when forming a quadratic from whole number roots?

Identify the roots

What factors form from roots $-4$ and $5$ ?

$(x + 4)(x - 5)$

Expanding $(x + 4)(x - 5) = 0$ using FOIL gives which equation?

$x^2 - x - 20 = 0$

If $x = \frac{a}{b}$ is a root, what is the factor?

$(bx - a)$

If $x = \frac{1}{2}$ is a root, what is the factor?

$(2x - 1)$

What equation forms from roots $-\frac{1}{4}$ and $3$ ?

$4x^2 - 11x - 3 = 0$

How do you verify your quadratic equation is correct?

Substitute roots; both should = zero

What is the standard form of a quadratic equation?

$ax^2 + bx + c = 0$

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