If the expression under the square root is negative, then the quadratic equation will have zero real solutions. It follows, then, that when there are no real solutions to a quadratic equation, the graph of the equation will have zero x-intercepts, meaning that the parabola will never intersect the x-axis.

Subsequently, question is, what is the condition for no solution? A system of linear equations can have no solution, a unique solution or infinitely many solutions. A system has no solution if the equations are inconsistent, they are contradictory. for example 2x 3y=10, 2x 3y=12 has no solution. is the rref form of the matrix for this system.

In this regard, what is a quadratic equation with no real solution?

An example of a quadratic function with no real roots is given by, f(x) = x2 − 3x 4. Notice that the discriminant of f(x) is negative, b2 −4ac = (−3)2− 4 · 1 · 4 = 9 − 16 = −7. This function is graphically represented by a parabola that opens upward whose vertex lies above the x-axis.

Which equation has no solution?

Be careful that you do not confuse the solution x = 0 with “no solution”. The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation.

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.

Secondly, when discriminant is zero then roots are? When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax2 bx c = 0 are real and equal.

Keeping this in consideration, how many solutions are there if the discriminant is zero?

one solution

How do you prove a quadratic has no real roots?

If the discriminant is greater than zero, this means that the quadratic equation has two real, distinct (different) roots. x2 - 5x 2. 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 3x2 2x 1.