jee-main 2022 Q81

jee-main · India · session1_27jun_shift2 Roots of polynomials Determine coefficients or parameters from root conditions

Let $\alpha , \beta$ be the roots of the equation $x ^ { 2 } - 4 \lambda x + 5 = 0$ and $\alpha , \gamma$ be the roots of the equation $x ^ { 2 } - ( 3 \sqrt { 2 } + 2 \sqrt { 3 } ) x + 7 + 3 \lambda \sqrt { 3 } = 0$. If $\beta + \gamma = 3 \sqrt { 2 }$, then $( \alpha + 2 \beta + \gamma ) ^ { 2 }$ is equal to

Let $\alpha , \beta$ be the roots of the equation $x ^ { 2 } - 4 \lambda x + 5 = 0$ and $\alpha , \gamma$ be the roots of the equation $x ^ { 2 } - ( 3 \sqrt { 2 } + 2 \sqrt { 3 } ) x + 7 + 3 \lambda \sqrt { 3 } = 0$. If $\beta + \gamma = 3 \sqrt { 2 }$, then $( \alpha + 2 \beta + \gamma ) ^ { 2 }$ is equal to

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