How can you tell if a quadratic equation has no real solutions?

If you get a positive number, the quadratic will have two unique solutions. If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.

How do you show a quadratic equation has no real roots?

The value of the discriminant shows how many roots f(x) has: – If b2 – 4ac > 0 then the quadratic function has two distinct real roots. – If b2 – 4ac = 0 then the quadratic function has one repeated real root. – If b2 – 4ac < 0 then the quadratic function has no real roots.

How can you tell from the graph of a quadratic function whether it has no real zeros?

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 do you tell if a graph has no real solution?

Look at the discriminant – if it is negative, there is no real solution to the quadratic. Look at the graph – if the parabola never touches the x-axis, there is no real solution to the quadratic.

How do you tell if a graph has no solutions?

If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.

What formula has no real roots?

A quadratic equation ax2 + bx + c = 0 has no real roots if discriminant < 0. Hence option A is the answer.

Is it possible for a quadratic inequality not to have a real solution?

Whenever you have a quadratic inequality where the associated quadratic equation does not have real solutions (that is, where the associated parabola does not cross the x-axis), the solution to the inequality will either be “all x” or “no x”, depending upon whether the parabola is on the side of the axis that you need.

What are real solutions in quadratic equations?

If the discriminant is equal to 0, the quadratic equation has 1 real solution. If the discriminant is less than 0, the quadratic equation has 0 real solutions.

What is an example of no solution?

The last type of equation is known as a contradiction, which is also known as a No Solution Equation. This type of equation is never true, no matter what we replace the variable with. As an example, consider 3x + 5 = 3x – 5. This equation has no solution.