Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Front

What do the variables a, b, and c represent in the quadratic formula?

Back

In the quadratic formula, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term in the quadratic equation.

Front

How do you determine the discriminant in a quadratic equation?

Back

The discriminant is calculated as D = b² - 4ac. It determines the nature of the roots of the quadratic equation.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real root (a repeated root).

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has no real roots, but two complex roots.

Front

How can you identify a, b, and c in the quadratic equation x² - 6x + 14?

Back

In the equation x² - 6x + 14, a = 1, b = -6, and c = 14.

Front

What is the first step in using the quadratic formula to solve for x?

Back

The first step is to identify the coefficients a, b, and c from the quadratic equation.

Front

How do you apply the quadratic formula to find the roots of the equation x² + 10x + 21 = 0?

Back

Identify a=1, b=10, c=21, then use the quadratic formula: x = (-10 ± √(10² - 4*1*21)) / (2*1).

Front

What are the roots of the equation x² + 10x + 21 = 0?

Back

The roots are x = -3 and x = -7.