Imaginary roots are solutions to quadratic equations with negative discriminants.
Imaginary Roots in Quadratic Equations
For a quadratic equation in the form ax2 + bx + c = 0,
the discriminant (Δ) is calculated as b2 – 4ac.
When the discriminant is negative, the quadratic equation has no real roots.
Instead, it has two complex roots, which are imaginary.
The discriminant is the part under the square root sign, which is (b2 – 4ac). If the discriminant is negative, the square root cannot be taken, and the answers are not real.
Formula for imaginary roots
Mathematically, if discriminant < 0, the roots are given by the formula:
x = (−b ± i √∣Δ∣) / 2a
where ‘i’ is the imaginary unit (√-1).
Understanding Imaginary Roots Imaginary roots provide solutions to quadratic equations that do not intersect the real number line. They are crucial in complex number theory and have applications in various mathematical and scientific fields.