If \(\alpha, \beta, \gamma, \delta\) are the roots of the equation \(x ^4+ x ^3+ x ^2+ x +1=0\), then \(\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}\) is equal to
- \(-4\)
- \(-1\)
- 1
- 4
The Correct Option is B
Solution and Explanation
The equation is equal to -1.
Therefore, The correct option is (B): -1
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Concepts Used:
Quadratic Equations
A polynomial that has two roots or is of degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b, and c are the real numbers.
Consider the following equation ax²+bx+c=0, where a≠0 and a, b, and c are real coefficients.
The solution of a quadratic equation can be found using the formula, x=((-b±√(b²-4ac))/2a)
Two important points to keep in mind are:
- A polynomial equation has at least one root.
- A polynomial equation of degree ‘n’ has ‘n’ roots.
Read More: Nature of Roots of Quadratic Equation
There are basically four methods of solving quadratic equations. They are:
- Factoring
- Completing the square
- Using Quadratic Formula
- Taking the square root