jee-main 2025 Q61

jee-main · India · session2_02apr_shift1 Roots of polynomials Determine coefficients or parameters from root conditions
Q61. If 2 and 6 are the roots of the equation $a x ^ { 2 } + b x + 1 = 0$, then the quadratic equation, whose roots are $\frac { 1 } { 2 a + b }$ and $\frac { 1 } { 6 a + b }$, is :
(1) $2 x ^ { 2 } + 11 x + 12 = 0$
(2) $x ^ { 2 } + 8 x + 12 = 0$
(3) $4 x ^ { 2 } + 14 x + 12 = 0$
(4) $x ^ { 2 } + 10 x + 16 = 0$
Q61. If 2 and 6 are the roots of the equation $a x ^ { 2 } + b x + 1 = 0$, then the quadratic equation, whose roots are $\frac { 1 } { 2 a + b }$ and $\frac { 1 } { 6 a + b }$, is :\\
(1) $2 x ^ { 2 } + 11 x + 12 = 0$\\
(2) $x ^ { 2 } + 8 x + 12 = 0$\\
(3) $4 x ^ { 2 } + 14 x + 12 = 0$\\
(4) $x ^ { 2 } + 10 x + 16 = 0$