Quadratic equations: factorising, completing the square and the formula

What is the standard form of a quadratic equation?

ax² + bx + c = 0, where a ≠ 0

Which statement is the zero-product property used when solving factorised quadratics?

If pq = 0, then p = 0 or q = 0

How does x² − 5x + 6 factorise?

(x − 2)(x − 3)

What are the solutions of x² − 5x + 6 = 0?

x = 2 or x = 3

Which is the correct factorisation of 2x² + 7x + 3?

(2x + 1)(x + 3)

Which factorisation uses the difference of two squares correctly?

x² − 16 = (x − 4)(x + 4)

Which identity is used to begin completing the square for x² + bx?

x² + bx = (x + b/2)² − (b/2)²

Write x² + 8x + 3 in completed-square form.

(x + 4)² − 13

After completing the square, x² + 6x − 7 = 0 becomes (x + 3)² = 16. What are its solutions?

x = 1 or x = −7

Which is the completed-square form of 2x² − 12x + 5?

2(x − 3)² − 13

What is the quadratic formula for ax² + bx + c = 0?

x = (−b ± √(b² − 4ac))/(2a)

For 3x² − 2x − 7 = 0, what are a, b and c?

a = 3, b = −2, c = −7

What does the discriminant b² − 4ac reveal about a quadratic equation?

The number and type of its roots

What does a discriminant of zero mean?

The equation has one repeated real root

Using the quadratic formula, what are the solutions of 2x² + x − 3 = 0?

x = 1 or x = −3/2

Why does x² + 2x + 5 = 0 have no real solutions?

Its discriminant is negative

A quadratic has roots −2 and 5. Which equation has these roots?

x² − 3x − 10 = 0

To solve x² = 9 by factorising, which equation should be formed first?

x² − 9 = 0