First 15 Nov 11

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial. It takes the form (a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b².

Front

How do you factor a difference of squares?

Back

A difference of squares can be factored using the formula a² - b² = (a + b)(a - b).

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 is the significance of the discriminant in a quadratic equation?

Back

The discriminant, given by the formula D = b² - 4ac, determines the nature of the roots of the quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root (a repeated root); if D < 0, there are no real roots.

Front

How do you complete the square for the expression x² - 6x?

Back

To complete the square, take half of the coefficient of x (which is -6), square it (which gives 9), and add and subtract it: x² - 6x + 9 - 9 = (x - 3)² - 9.

Front

What is the factored form of the quadratic expression x² - 5x + 6?

Back

The factored form is (x - 2)(x - 3).

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as a + b or x² - 4.

Front

What does it mean for a quadratic to be factorable?

Back

A quadratic is factorable if it can be expressed as the product of two binomials with real coefficients.

Front

What is the relationship between the roots and the coefficients of a quadratic equation?

Back

The sum of the roots (r₁ + r₂) is equal to -b/a, and the product of the roots (r₁ * r₂) is equal to c/a, according to Vieta's formulas.

Front

How do you identify a perfect square trinomial from an expression?

Back

A perfect square trinomial can be identified if it can be expressed in the form a² ± 2ab + b², where a and b are real numbers.