How do you know when a quadratic equation will have no solution?

A quadratic equation has no solution when the discriminant is negative. From an algebra standpoint, this means b2 < 4ac. Visually, this means the graph of the quadratic (a parabola) will never touch the x axis.

What do the solutions of a quadratic equation tell us?

The “solutions” to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions (as shown in this graph). Just plug in the values of a, b and c, and do the calculations.

Which of the given integers will complete the quadratic equation?

The solutions to the equation are x=−12+i√72 x = − 1 2 + i 7 2 and x=−12−i√72 x = − 1 2 − i 7 2 . . Notice they are written in standard form of a complex number. When a solution is a complex number, you must separate the real part from the imaginary part and write it in standard form.

Is it possible for a quadratic equation to have infinite solutions?

Infinite Solutions Two quadratic equations that overlap but have different equations have two solutions. If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.

What is a quadratic function with 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. An example of a quadratic function with no real roots is given by, f(x) = x2 − 3x + 4.

What does the quadratic equation represent?

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b and c being constants, or numerical coefficients, and x being an unknown variable.

What does the solution of a quadratic equation represent on a graph?

The solutions to a quadratic equation are the values of x where the graph crosses the x-axis. These are the x-intercepts! The graph will cross up to two times.

What does it mean to solve by completing the square?

Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary. For example, consider x2 + 6x + 7. Start by noting that. (x + 3)2 = (x + 3)(x + 3) = x2 + 6x + 9. This is 2 more than our expression, so x.

Do quadratic equations have two solutions?

A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions. All methods start with setting the equation equal to zero.

What does it mean to have infinite solutions?

So far we have looked at equations where there is exactly one solution. No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.

How do you find infinite solutions?

If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.

How do you solve quadratic equations by factoring?

» 1. Solving Quadratic Equations by Factoring 1. Solving Quadratic Equations by Factoring (b) 5 + 3t − 4.9t 2 = 0 is a quadratic equation in quadratic form. [This equation arose from finding the time when a projectile, being acted on by gravity, hits the ground.] (c) (x + 1) 2 = 4 is a quadratic equation but not in quadratic form.

What is the general form of a quadratic equation?

The general form of a quadratic equation is. ax 2 + bx + c = 0. where x is the variable and a, b & c are constants. (a) 5x 2 − 3x − 1 = 0 is a quadratic equation in quadratic form where. `a = 5`, `b = -3`, `c = -1`. (b) 5 + 3t − 4.9t 2 = 0 is a quadratic equation in quadratic form.

How do you solve a quadratic equation with no solution?

The quadratic formula can also be used to solve quadratic equations whose roots are imaginary numbers, that is, they have no solution in the real number system. Solve for x: x ( x + 2) + 2 = 0, or x 2 + 2 x + 2 = 0. Since the discriminant b 2 – 4 ac is negative, this equation has no solution in the real number system.

What is an example of a non-quadratic equation?

Examples of NON-quadratic Equations. bx − 6 = 0 is NOT a quadratic equation because there is no x 2 term. x 3 − x 2 − 5 = 0 is NOT a quadratic equation because there is an x 3 term (not allowed in quadratic equations).