Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of the quadratic equation. If D > 0, there are two real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

How do you determine the number of real solutions from the discriminant?

Back

If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. If it is negative, there are no real solutions.

Front

What is the value of the discriminant for the equation 4x² + 6x - 4 = 0?

Back

The discriminant is calculated as D = b² - 4ac = (6)² - 4(4)(-4) = 36 + 64 = 100.

Front

What are the solutions to the equation 2x² + 2x - 12 = 0 using the quadratic formula?

Back

The solutions are x = 2 and x = -3.

Front

What does it mean if a quadratic equation has no real solutions?

Back

It means that the graph of the quadratic function does not intersect the x-axis, indicating that the roots are complex or imaginary.

Front

How can you solve the quadratic equation x² + x - 56 = 0 using the quadratic formula?

Back

Using the quadratic formula, the solutions are x = 7 and x = -8.

Front

What is the significance of the coefficients a, b, and c in the quadratic formula?

Back

The coefficients a, b, and c represent the numerical values in the quadratic equation ax² + bx + c = 0, where 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

What happens to the number of solutions if the coefficient 'a' in a quadratic equation is zero?

Back

If 'a' is zero, the equation is no longer quadratic but linear, and it can have either one solution or no solution depending on the value of 'b'.

Front

What is the vertex of a quadratic function and how is it related to the solutions?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, and it can provide information about the solutions; if the vertex is above the x-axis, there may be no real solutions.