Let one root of the quadratic equation in \(x\):

\(\left({k}^{2}-15k+27\right){x}^{2}+9(k-1)x+18=0\)

be twice the other. Then the length of the latus rectum of the parabola \({y}^{2}=6kx\) is equal to:

[JEE Main 2026, 6 Apr (Shift 1)]

Question

Let one root of the quadratic equation in \(x\):

\(\left({k}^{2}-15k+27\right){x}^{2}+9(k-1)x+18=0\)

be twice the other. Then the length of the latus rectum of the parabola \({y}^{2}=6kx\) is equal to:

[JEE Main 2026, 6 Apr (Shift 1)]

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Let one root of the quadratic equation in \(x\): \(\left({k}^{2}-15k+27\right){x}^{2}+9(k-1)x+18=0\) be twice the other.…