Question

which of the following values of the discriminant of a quadratic equation has imaginary solutions?

Answer 1

When the discriminant has the negative values, then discriminant of a quadratic equation has an imaginary solutions.

Answer 2

$\mathrm{D<0}$, where $\mathrm{D}$ is discriminant

When $\mathrm{D<0}$, a quadratic equation will have imaginary solutions.

Explanation:

Let us take a quadratic equation

$\mathrm{\quad ax^{2}+bx+c=0}$,

where $\mathrm{a\neq 0}$ and $\mathrm{a,b,c\in\mathbb{R}}$

Then its discriminant, $\boxed{\mathrm{D=b^{2}-4ac}}$

Condition 1.

• When $\mathrm{D>0}$, the given quadratic equation will have two unequal and real roots.

Condition 2.

• When $\mathrm{D=0}$, the given quadratic equation will have two equal and real roots.

Condition 3.

• When $\mathrm{D<0}$, the given quadratic equation will have two unequal and imaginary roots.

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