Question:medium
Let \( \alpha, \beta \) be the roots of the equation \( x^2 - 3x + r = 0 \), and \( \frac{\alpha}{2}, 2\beta \) be the roots of the equation \( x^2 + 3x + r = 0 \).
If the roots of the equation \( x^2 + 6x = m \) are \( 2\alpha + \beta + 2r \) and \( \alpha - 2\beta - \frac{r}{2} \), then \( m \) is equal to:
Let \( \alpha, \beta \) be the roots of the equation \( x^2 - 3x + r = 0 \), and \( \frac{\alpha}{2}, 2\beta \) be the roots of the equation \( x^2 + 3x + r = 0 \).
If the roots of the equation \( x^2 + 6x = m \) are \( 2\alpha + \beta + 2r \) and \( \alpha - 2\beta - \frac{r}{2} \), then \( m \) is equal to:
Updated On: Apr 10, 2026
- -135
- -567
- 135
- 567
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
