jee-main 2023 Q61

jee-main · India · session1_29jan_shift1 Roots of polynomials Determine coefficients or parameters from root conditions

Let $\lambda \neq 0$ be a real number. Let $\alpha , \beta$ be the roots of the equation $14 x ^ { 2 } - 31 x + 3 \lambda = 0$ and $\alpha , \gamma$ be the roots of the equation $35 x ^ { 2 } - 53 x + 4 \lambda = 0$. Then $\frac { 3 \alpha } { \beta }$ and $\frac { 4 \alpha } { \gamma }$ are the roots of the equation :
(1) $7 x ^ { 2 } + 245 x - 250 = 0$
(2) $7 x ^ { 2 } - 245 x + 250 = 0$
(3) $49 x ^ { 2 } - 245 x + 250 = 0$
(4) $49 x ^ { 2 } + 245 x + 250 = 0$

Let $\lambda \neq 0$ be a real number. Let $\alpha , \beta$ be the roots of the equation $14 x ^ { 2 } - 31 x + 3 \lambda = 0$ and $\alpha , \gamma$ be the roots of the equation $35 x ^ { 2 } - 53 x + 4 \lambda = 0$. Then $\frac { 3 \alpha } { \beta }$ and $\frac { 4 \alpha } { \gamma }$ are the roots of the equation :\\
(1) $7 x ^ { 2 } + 245 x - 250 = 0$\\
(2) $7 x ^ { 2 } - 245 x + 250 = 0$\\
(3) $49 x ^ { 2 } - 245 x + 250 = 0$\\
(4) $49 x ^ { 2 } + 245 x + 250 = 0$

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