The maximum number of real distinct roots that a quartic equation can have is 4.
Quartic Equation or 4th Degree Equation
What is quartic equation?
Quartic polynomial, which is an integer-coefficient polynomial with a four-degree maximum. The fourth-degree variable's coefficient cannot be zero.
General equation for quartic polynomial:
The general form for 4th degree equation is
\(ax^{4} +bx^{3} +cx^{2} +dx+e=0\)
Where, \(a
eq 0\)
What is real roots?
A root is a value which when replace a variable in an equation with a single variable so that the equation still holds true. It is the "solution" to the problem, to put it another way. If it is also a real number, it is referred to as a real root.
What is imaginary roots?
The simplest imaginary number is i = \(\sqrt{1}\), which is used to express imaginary roots.
Maximum real distinct roots:
Consider the quartic equation,
\(ax^{4} +bx^{3} +cx^{2} +dx+e=0\)
As the highest power in the equation is 4. So, the total number of roots for the equation is also 4.
Therefore, the number of real distinct roots possible for the equation is also 4.
To know more about how to solve a quadratic equation?, here
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