Solving Quadratics by Factoring Trinomials

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a trinomial?

Back

Factoring a trinomial involves rewriting it as a product of two binomials.

Front

Solve: a² + 2a - 24 = 0

Back

a = -6, 4

Front

Solve: x² - 49 = 0

Back

x = -7, 7

Front

Solve: 16a² - 9 = 0

Back

a = -3/4, 3/4

Front

What are the roots of the equation x² + 12x + 35 = 0?

Back

x = -5 or x = -7

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).