Question

How many complex roots does a cubic equation have?

Answer 1

Hint: Here we will use the basic concept of the roots and find the number of roots a cubic equation can have. Then we will use the theory of the imaginary or the complex roots that a real root can be written as a complex root. Then by using this, we will get the number of complex roots a cubic equation can have.

Complete step by step solution:
We know that the number of roots of an equation is equal to the value of the highest exponent of the equation’s variable.
Cubic equation is the equation which has the highest exponent of the variable as 3. Therefore the numbers of roots of a cubic equation are three and these roots can be real roots or the complex roots.
We know that any real root can also be written in the complex form i.e. with the imaginary part \[a + \left( 0 \right)i\].
Therefore, we can say that a cubic equation can have three complex roots.

Hence, three complex roots a cubic equation can have.

Note:
Roots are those values of the equation where the value of the equation becomes zero. For any equation, numbers of roots are always equal to the value of the highest exponent of the variable x. A linear equation is the equation in which the highest exponent of the variable x is one. A quadratic equation is an equation in which the highest exponent of the variable x is two and a quadratic equation has only two roots.
Real value is a number which has some real or discrete or possible value. But imaginary value is the number with a real number multiplied with an imaginary part \[i\].