Determining the Nature of Quadratic Roots

What is the standard form of a quadratic equation?

• ax^2 + bx = 0

• ax^3 + bx^2 + c = 0

• ax^2 + bx + c = 0

• ax + b = 0

Which of the following methods is NOT used to solve quadratic equations?

• Extracting square roots

• Factoring

• Completing the square

• Using logarithms

What is the expression inside the radical in the quadratic formula called?

• Determinant

• Coefficient

• Discriminant

• Radical

What does a discriminant value of zero indicate about the roots of a quadratic equation?

• The roots are real, rational, and equal

• The roots are complex

• The roots are real, irrational, and unequal

• The roots are imaginary

If the discriminant is positive and a perfect square, what is the nature of the roots?

• Real, rational, and equal

• Imaginary

• Real, irrational, and unequal

• Real, rational, and unequal

What is the nature of the roots if the discriminant is positive but not a perfect square?

• Imaginary

• Real, irrational, and unequal

• Real, rational, and unequal

• Real, rational, and equal

In the first example, what are the values of a, b, and c for the equation x^2 - 4x + 4 = 0?

• a = 1, b = -4, c = 4

• a = 1, b = 4, c = -4

• a = -1, b = 4, c = 4

• a = 1, b = -4, c = -4

What is the discriminant of the equation x^2 - 4x + 4 = 0?

• 4

• 8

• 0

• 16

In the second example, what is the discriminant of the equation x^2 + 7x + 10 = 0?

• 49

• 9

• 7

• 40

What is the nature of the roots for the equation x^2 + 7x + 10 = 0?

• Imaginary

• Real, rational, and equal

• Real, rational, and unequal

• Real, irrational, and unequal