jee-main 2018 Q61

jee-main · India · 15apr_shift1 Roots of polynomials Vieta's formulas: compute symmetric functions of roots

If $\lambda \in \mathrm { R }$ is such that the sum of the cubes of the roots of the equation, $x ^ { 2 } + ( 2 - \lambda ) x + ( 10 - \lambda ) = 0$ is minimum, then the magnitude of the difference of the roots of this equation is
(1) 20
(2) $2 \sqrt { 5 }$
(3) $2 \sqrt { 7 }$
(4) $4 \sqrt { 2 }$

If $\lambda \in \mathrm { R }$ is such that the sum of the cubes of the roots of the equation, $x ^ { 2 } + ( 2 - \lambda ) x + ( 10 - \lambda ) = 0$ is minimum, then the magnitude of the difference of the roots of this equation is\\
(1) 20\\
(2) $2 \sqrt { 5 }$\\
(3) $2 \sqrt { 7 }$\\
(4) $4 \sqrt { 2 }$

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