Question

What do two complex roots mean?

Answer 1

Two Complex roots:

• The roots of a quadratic equation are the values that satisfy the equation.
• Since the quadratic equations are of the order $2,$there will be two values where the curve intersects the X-axis.
• The determinant determines the nature of the roots.
• For a quadratic equation of the form $a{x}^2+bx+c$, determinant $\mathit{D}\mathbf{=}{\mathit{b}}^{\mathbf{2}}\mathbf{-}\mathbf{4}\mathit{a}\mathit{c}$.
• Based on the nature of the determinant, the roots can be:

1. If $D>0,$the roots are real and distinct.
2. If $D=0,$the roots are real and equal.
3. If $D<0,$the roots are complex or imaginary.whenever a complex number is a root of a polynomial with real coefficients, its complex conjugate is also a root of that polynomial. i.e. if $a+ib$ is root of polynomial equation then $a-ib$ is also root of polynomial equation.

So,complex roots always comes in pair for polynomial equation.

Hence, the meaning of two complex roots is explained.