What happens if discriminant is negative in quadratic formula?

If the discriminant is negative, that means there is a negative number under the square root in the quadratic formula. You may have learned in the past that you "can't take the square root of a negative number." The truth is that you can take the square root of a negative number, but the answer is not real.

What happens if the discriminant of a quadratic equation is negative?

If the discriminant of an equation is negative, then the roots will be imaginary.

What to do if the discriminant is negative?

The discriminant is the term underneath the square root in the quadratic formula and tells us the number of solutions to a quadratic equation. If the discriminant is positive, we know that we have 2 solutions. If it is negative, there are no solutions and if the discriminant is equal to zero, we have one solution.

Does a negative discriminant mean no solutions?

If the discriminant is negative, then the quadratic equation has no real solution. The discriminant is the expression b² – 4ac under the radical in the quadratic formula. Its sign can tell us the nature of the solutions of the corresponding quadratic equation.

Which is the graph of a quadratic equation that has a negative discriminant?

If the discriminant is negative, that means that the roots of the quadratic function are not real numbers. In other words, the graph has no x-intercepts. Of the four choices that are given, choices (B) and (C) are both possible. If the discriminant is negative the roots are complex.

Negative Underneath Root in Quadratic Formula (Imaginary Solutions)

Can a be negative in a quadratic equation?

Math Skills - The Quadratic Equation. Many times in Chemistry, e.g. when solving equilibrium problems, a quadratic equation results. It has the general form: 0 = ax² + bx + c Each of the constant terms (a, b, and c) may be positive or negative numbers.

What is the nature of the roots of quadratic equation if the discriminant is negative?

If the discriminant of the quadratic equation is negative, then the square root of the discriminant will be undefined.

What happens if the discriminant is less than zero?

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.

When the discriminant is negative then the nature of the roots is?

The roots may be imaginary, real, unequal or equal. If the discriminate is negative, the roots will be imaginary.

How many solutions does a quadratic equation have if the discriminant is negative?

Because the discriminant is negative, the quadratic equation has no real number solutions, only two imaginary ones.

How many roots if discriminant is negative?

If the discriminant is: Positive, you have 2 real roots. Zero, you have 1 real root. Negative, you have 0 real roots(no solution).

What happens if the discriminant is greater than zero?

When the discriminant is greater than 0, there are two distinct real roots. When the discriminant is equal to 0, there is exactly one real root. When the discriminant is less than zero, there are no real roots, but there are exactly two distinct imaginary roots.

How do you tell if a quadratic equation is positive or negative?

A positive quadratic coefficient causes the ends of the parabola to point upward. A negative quadratic coefficient causes the ends of the parabola to point downward.

What is the nature of the quadratic equation if the discriminant is less than zero?

When discriminant is equal to zero, the roots are equal and real. When discriminant is less than zero, the roots are imaginary.

When the discriminant of a quadratic equation is positive What is the nature of the roots?

Clearly, the discriminant of the given quadratic equation is positive and a perfect square. Therefore, the roots of the given quadratic equation are real, rational and unequal. 2.

How does the discriminant determine the nature of the roots?

Determining the Nature of Roots

The discriminant is negative, so the equation has two non-real solutions. The discriminant is 0, so the equation has a double root. If the discriminant is a perfect square, then the solutions to the equation are not only real, but also rational.

What does it mean when the discriminant is negative?

A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

What happens when a is negative in a quadratic function?

If a is negative, the graph of the parabola opens down instead of up. The b-value of a parabola helps to determine the rate at which the parabola increases and decreases, and it also helps to determine the position of the vertex of the parabola. The c-value determines the y-intercept of a quadratic function.

What does a negative discriminant look like?

If the discriminant is negative, that means there is a negative number under the square root in the quadratic formula. You may have learned in the past that you "can't take the square root of a negative number." The truth is that you can take the square root of a negative number, but the answer is not real.

What do you notice about the graph of a parabola when its discriminant is negative?

The solution occurs at that point. If there are any real solutions, the discriminant must be zero or positive. But if the graph does NOT touch the x-axis, then there are no real solutions, which means that the discriminant is negative. So you are looking for a graph that does NOT touch the x-axis.

What is true about the solutions to a quadratic equation if the discriminant is less than zero?

If the discriminant is less than 0, the quadratic equation has 0 real solutions. (Instead of real solutions, the quadratic equation has 2 imaginary solutions.)

What does the discriminant tell us about a quadratic function?

The discriminant gives us important information about the quadratic equation. First, it can tell us how many solutions the quadratic equation has. It can also tell us how many times the graph crosses the x-axis and if the solutions are real or complex.