Quadratic Formula and Discriminant

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (D) is given by D = b² - 4ac. It indicates the nature of the roots of the quadratic equation: if D > 0, there are 2 distinct real solutions; if D = 0, there is 1 real solution; if D < 0, there are no real solutions.

Front

Identify the values of a, b, and c in the equation: 3x² + 5x - 2 = 0.

Back

a = 3, b = 5, c = -2.

Front

What is the value of a in the equation: x² - 4x + 4 = 0?

Back

a = 1.

Front

If the discriminant is 0, how many solutions does the quadratic equation have?

Back

1 solution (the roots are real and equal).

Front

What is the value of b in the equation: 2x² + 3 = 0?

Back

b = 0.

Front

How do you calculate the discriminant for the equation: 5x² - 3x + 2 = 0?

Back

D = b² - 4ac = (-3)² - 4(5)(2) = 9 - 40 = -31.

Front

What does it mean if the discriminant is negative?

Back

It means the quadratic equation has no real solutions (the roots are complex).

Front

For the equation: 4x² + 2x - 6 = 0, what are the values of a, b, and c?

Back

a = 4, b = 2, c = -6.

Front

What is the significance of the term 'quadratic'?

Back

A quadratic refers to a polynomial of degree 2, typically in the form ax² + bx + c.