Find Discriminant & Number of Solutions

Front

What is the discriminant in a quadratic equation?

Back

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

Front

Calculate the discriminant for the equation: -3x² - 5x + 15 = 7

Back

121

Front

How many solutions does the quadratic equation 2x² - 16x + 33 = 0 have?

Back

None

Front

How many solutions does the quadratic equation x² - 12x + 36 = 0 have?

Back

One

Front

Calculate the discriminant for the equation: 2x² - 10x + 5 = 7

Back

116

Front

How many solutions does the quadratic equation -x² + 2x + 1 = 0 have?

Back

Two

Front

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

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

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

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

Front

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

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.

Front

If a quadratic equation has a discriminant of 0, what can you say about its graph?

Back

The graph of the quadratic equation touches the x-axis at one point (the vertex) and does not cross it.