Quadratic Equations
If α, β are roots of x² - 3x + 1 = 0, then the value of α³ + β³ is
Select the correct option:
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More complex numbers and quadratic equations Practice Questions
If the roots of the equation x² - 5x + 6 = 0 are α and β, then α + β equals
If the roots of the equation x² - 5x + 6 = 0 are α and β, then α + β equals
The discriminant of the quadratic equation 2x² - 7x + 3 = 0 is
The discriminant of the quadratic equation 2x² - 7x + 3 = 0 is
If α and β are the roots of x² - px + q = 0, then the equation whose roots are α² and β² is
If α and β are the roots of x² - px + q = 0, then the equation whose roots are α² and β² is
For what value of k does the equation x² + kx + 16 = 0 have equal roots?
For what value of k does the equation x² + kx + 16 = 0 have equal roots?
The set of all complex numbers z satisfying the equation given by the ratio condition arg of the qua...
The set of all complex numbers z satisfying the equation given by the ratio condition arg of the qua...
If the equation x^2 - (k - 3)x + k = 0 has both roots real, then the set of all real values of the p...
If the equation x^2 - (k - 3)x + k = 0 has both roots real, then the set of all real values of the p...
Among all complex numbers z lying on the circle defined by |z| = 1, the maximum value attained by th...
Among all complex numbers z lying on the circle defined by |z| = 1, the maximum value attained by th...
If alpha and beta are roots of x^2 - 2x + 4 = 0, then the value of the symmetric expression alpha cu...
If alpha and beta are roots of x^2 - 2x + 4 = 0, then the value of the symmetric expression alpha cu...
The values of the real parameter m for which the quadratic equation (m + 1)x^2 + 2(m + 3)x + (m + 8)...
The values of the real parameter m for which the quadratic equation (m + 1)x^2 + 2(m + 3)x + (m + 8)...
For any complex number z, the expression z multiplied by its conjugate z-bar is always equal to whic...
For any complex number z, the expression z multiplied by its conjugate z-bar is always equal to whic...
If two complex numbers have moduli 2 and 5 and arguments 40 degrees and 80 degrees respectively, the...
If two complex numbers have moduli 2 and 5 and arguments 40 degrees and 80 degrees respectively, the...
If the two quadratic equations x^2 + bx + c = 0 and x^2 + cx + b = 0, with b not equal to c, share e...
If the two quadratic equations x^2 + bx + c = 0 and x^2 + cx + b = 0, with b not equal to c, share e...
Browse all complex numbers and quadratic equations questions →
About This Question
- Subject
- mathematics
- Chapter
- complex numbers and quadratic equations
- Topic
- quadratic equations
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
18
- Vieta: α+β=3,αβ=1.
- Algebraic Identity: α3+β3=(α+β)3−3αβ(α+β).
- Substitution:
- α3+β3=(3)3−3(1)(3)
- =27−9=18.
- Alternatively, since α2−3α+1=0, multiplying by α gives α3−3α2+α=0, which can lead to a recursive solution.
This medium difficulty mathematics question is from the chapter complex numbers and quadratic equations, covering the topic of quadratic equations. It appeared in the 2025 exam.
Looking for more practice? Explore all mathematics questions or browse complex numbers and quadratic equations questions on RankGuru.