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

Asked by: Jann Mittermaier

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.

Also asked, 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.

28 Related Question Answers Found

What does no real solution mean in math?

This means that there are no real answers; the solution are two imaginary numbers. The answers are and. These answers may or may not be solutions to the original equations.

What makes a real solution?

A real solution is a solution to something like a quadratic equation involving only real numbers, not imaginary or complex numbers. A distinct solution, in the example of a quadratic, is where the curve crosses the X axis in two separate, distinct places.

How do you know if an equation has infinitely many solutions?

A linear equation has infinitely many solutions (in the variable x) if and only if both the overall coefficients of x on the two sides are equal, and the overall constants on the two sides are equal.

What does infinitely many solutions mean?

Infinite Solutions. The first is when we have what is called infinite solutions. This happens when all numbers are solutions. This situation means that there is no one solution. The equation 2x + 3 = x + x + 3 is an example of an equation that has an infinite number of solutions.

What does a nonlinear equation look like?

A non-linear equation look like a curve when graphed. It has a variable slope value. The degree of a non-linear equation is at least 2 or other higher integer values. With the increase in the degree of the equation, the curvature of the graph increases.

How many solutions does a quadratic equation have?

As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 – 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

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 3×2 + 2x + 1.

How do you solve system of equations?

Follow the steps to solve the problem. Step 1: Multiply the entire first equation by 2. Step 2: Rewrite the system of equations, replacing the first equation with the new equation. Step 3: Add the equations. Step 4: Solve for x. Step 5: Find the y-value by substituting in 3 for x in either equation.

How many solutions does a parabola have?

Answer and Explanation: The equation of a parabola can have one, two, or no solutions. By definition, the roots, or solutions, of a parabola’s equation are equal to the x-va

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