The statement should should read a quadratic equation with real coefficients can’t have only one imaginary root. The reason being in x2+ax+c=0 x 2 + a x + c = 0 because −a is sum of the roots and c is product of the roots. But a & c are both real numbers, that is impossible if only one of the roots were imaginary.

## Why a quadratic equation Cannot have one real root and one complex root?

A quadratic equation may take complex values for x but the coefficients are always real. This makes both b and c complex, which is not allowed as they have to be real. This is the reason why if quadratic equations have complex roots, they are in pairs and form complex conjugates.

## Can you have one imaginary solution?

Answer Expert Verified A quadratic equation cannot have one imaginary solution because of the discriminant enclosed in a radical. The discriminant, √(b² – 4ac), determines the nature of the roots and it can only be either 2 real roots, 1 real solution or 2 imaginary roots.

## How can you tell if a quadratic equation will have a complex solution?

If the discriminant equals 0, then the equation has one real solution, a double root. If the discriminant is less than 0, then the equation has two complex solutions.

## What is a real solution for a quadratic equation?

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.

## How can we use the discriminant to determine the types of zeros a quadratic equation will have?

The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. 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.

## How do you use the discriminant in a quadratic equation?

The discriminant is the part under the square root in the quadratic formula, b²-4ac. If it is more than 0, the equation has two real solutions. If it’s less than 0, there are no real solutions. If it’s equal to 0, there is one real solution.

## How many solutions are there if the discriminant is zero?

It tells you the number of solutions to a quadratic equation. If the discriminant is greater than zero, there are two solutions. If the discriminant is less than zero, there are no solutions and if the discriminant is equal to zero, there is one solution.

## How do you prove something has no real solutions?

If the discriminant is less than 0, the equation has no real solution. Looking at the graph of a quadratic equation, if the parabola does not cross or intersect the x-axis, then the equation has no real solution. And no real solution does not mean that there is no solution, but that the solutions are not real numbers.