Solving equations with squares and cubes

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the solutions to the equation x² = k, where k is a positive number?

Back

The solutions are x = ±√k.

Front

What is the solution to the equation x² = 0?

Back

The solution is x = 0.

Front

What is the significance of a negative number under a square root in an equation?

Back

A negative number under a square root indicates that there are no real solutions to the equation.

Front

How do you solve the equation 10 - 3a² = -2?

Back

Rearranging gives 3a² = 12, so a² = 4, leading to a = ±2.

Front

What is the value of -6²?

Back

The value of -6² is -36, as the negative sign is not included in the squaring.

Front

What does it mean if an equation has no solution?

Back

It means that there are no values of the variable that satisfy the equation.

Front

What is the cube root of -512?

Back

The cube root of -512 is -8.

Front

How do you determine the solutions for x² = 16?

Back

Taking the square root gives x = ±4.

Front

What is the relationship between the coefficients of a quadratic equation and its graph?

Back

The coefficients determine the shape, direction, and position of the parabola represented by the quadratic equation.