Question:medium
The equations \( x^5 + ax + 1 = 0 \) and \( x^6 + ax^2 + 1 = 0 \) have a common root. Then \( a \) is equal to:
The equations \( x^5 + ax + 1 = 0 \) and \( x^6 + ax^2 + 1 = 0 \) have a common root. Then \( a \) is equal to:
Show Hint
To find common roots, try to make the highest degree terms equal in both equations and then subtract them. This often reduces the problem to a much lower degree equation.
Updated On: May 1, 2026
- \( -4 \)
- \( -2 \)
- \( -3 \)
- \( -1 \)
- \( 0 \)
Show Solution
The Correct Option is B
Solution and Explanation
Was this answer helpful?
0
Top Questions on Quadratic Equations
- The equation \( (\cos p - 1)x^2 + (\cos p)x + \sin p = 0 \), where \( x \) is a variable with real roots. Then the interval of \( p \) may be any one of the following:
- MHT CET - 2024
- Mathematics
- Quadratic Equations
- If the roots of the quadratic equation \( x^2 - 7x + 12 = 0 \) are \( \alpha \) and \( \beta \), then the value of \( \alpha + \beta \) is:
- MHT CET - 2025
- Mathematics
- Quadratic Equations
- Find the roots of the quadratic equation $ x^2 - 5x + 6 = 0 $.
- MHT CET - 2025
- Mathematics
- Quadratic Equations
- Find the sum of the roots of the quadratic equation $ 2x^2 - 5x + 3 = 0 $.
- MHT CET - 2025
- Mathematics
- Quadratic Equations
- Want to practice more? Try solving extra ecology questions todayView All Questions
