When the discriminant is 0 is it rational or irrational?

5 (double root) Page 18 If the value of the discriminant is zero, the equation will have 1 real, root; it will be a double root. If the value of the discriminant is 0, the roots will be rational. Last but not least, the fourth equation.

What happens if discriminant is equal to zero?

When the discriminant is equal to 0, there is exactly one real root. When the discriminant is less than zero, there are no real roots, but there are exactly two distinct imaginary roots. In this case, there is exactly one real root. This value of x is the one distinct real root of the given equation.

How do you know if a discriminant is rational or irrational?

If the discriminant is positive and is a perfect square (ex. 36,121,100,625 ), the roots are rational. If the discriminant is positive and is not a perfect square (ex. 84,52,700 ), the roots are irrational.

What is an irrational solution?

Irrational solutions – An irrational number is a number that cannot be written as a fraction. In these cases, the equation does not have a perfect square, but the solutions can be found by taking the square root and rounding.

What if the discriminant is less than zero?

If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.

How many solutions does a discriminant of 0 have?

two solutions
It tells you the number of solutions to a quadratic equation. If the discriminant is greater than zero, there are two solutions. If the discriminant is less than zero, there are no solutions and if the discriminant is equal to zero, there is one solution.

Why is the discriminant greater than zero?

If the discriminant is greater than zero, this means that the quadratic equation has no real roots. Therefore, there are no real roots to the quadratic equation 3×2 + 2x + 1. If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots.

Why is discriminant less than 0 for increasing function?

If the discriminant is less than zero, than there are two distinct complex solutions to a*x^2 + b*x + c = 0 and there are no x-intercepts for the graph. So if the discriminant is negative, then the quadratic is either always positive or always negative.

What does it mean if the discriminant is 0?

What happens if the discriminant is 0? The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

When the discriminant is zero the equation has exactly two real solutions?

When the discriminant is equal to zero, the solution to the equation is equal to [math]\\frac {-b} {2a} [/math] As you know, if the discriminant is negative, the equation has exactly two imaginary solutions, and if the discriminant is positive, the equation has exactly two real solutions.

What is the discriminant of a quadratic equation?

The discriminant provides critical information regarding the number of the solutions of any quadratic equation prior to solving to find the solutions. b² − 4ac = 0, Discriminant is equal to zero.

What is the significance of the discriminant?

The discriminant provides critical information regarding the number of the solutions of any quadratic equation prior to solving to find the solutions. Number of Solutions of a Quadratic Equation: b² − 4ac > 0, Discriminant is greater than zero, Positive Discriminant: Two Real Solutions