# How do you know if a quadratic equation has no solution? asked in category: General Last Updated: 4th June, 2020

# How do you know if a quadratic equation has no solution?

Use the discriminant to determine whether the quadratic equation has two, one, or no solutions. a = 1, b = -4, and c = 10. The result is a negative number. The discriminant is negative, so the quadratic equation has no solution.

Keeping this in view, how do you know if an equation has no real solutions?

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.

Secondly, 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.

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.