Let α, β be the roots of the equation x²-3x+r=0, and (α)/2, 2β be the roots of the equation x²+3x+r=0. If the roots of the equation x²+6x=m are 2α+β+2r and α-2β-r/2, then m is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2026 Mathematics question

JEE Main 2026 · 2 Apr, Evening shift · Q1

JEE Main 20262 Apr, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

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 :

JEE Main 2026 · 2 Apr, Evening shift · Q1

JEE Main 20262 Apr, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

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 :