Discriminant of Quadratic Equations

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is a value calculated from the coefficients of a quadratic equation in the form ax² + bx + c, given by the formula D = b² - 4ac.

Front

What does the discriminant tell us about the solutions of a quadratic equation?

Back

The discriminant indicates the nature of the roots: if D > 0, there are 2 distinct real solutions; if D = 0, there is 1 real solution (a repeated root); if D < 0, there are no real solutions.

Front

For the quadratic equation x² - 7x + 2 = 15, what is the value of a?

Back

1

Front

Use the quadratic formula to find the solutions for y = -x² - 5x + 12.

Back

The solutions are -6.77 and 1.77.

Front

What is the value of b in the equation 5x² - 11 = 0?

Back

0

Front

Calculate the discriminant for the equation x² - 6x + 9 = 0 and state the number of solutions.

Back

The discriminant is 0, indicating 1 solution.

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.

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, found at the coordinates (h, k) where h = -b/(2a) and k is the value of the function at h.

Front

How do you determine if a quadratic equation has real solutions?

Back

By evaluating the discriminant: if D = b² - 4ac is non-negative, the equation has real solutions.