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MathsJEE Main 2 Apr 2026, Shift 2·Q1·MCQ·Moderate

Quadratic Equations · Relation between roots and coefficients

Let α,β\alpha, \beta be the roots of the equation x2−3x+r=0x^2 - 3x + r = 0, and α2,2β\dfrac{\alpha}{2}, 2\beta be the roots of the equation x2+3x+r=0x^2 + 3x + r = 0. If the roots of the equation x2+6x=mx^2 + 6x = m are 2α+β+2r2\alpha + \beta + 2r and α−2β−r2\alpha - 2\beta - \dfrac{r}{2}, then mm is equal to:
  1. (1)−135-135
  2. (2)−567-567
  3. (3)135
  4. (4)567

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