If the equation $2 x^{3} - 9 x^{2} + 12 x - k = 0$ has two equal roots, then $k$ is equal to

- 7

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7

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- 20

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20

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Solution

The correct options are
A $7$
B $20$
Let $α, α, β$ be the roots.
We have $α + α + β = \frac{9}{2},$
$α^{2} β = \frac{k}{2}$
$α^{2} + 2 α β = 6$
On solving these 3 equations we get $α = 1 \to β = \frac{7}{2} .$
or $α = 2 \to β = \frac{5}{2} .$
$∴ k = 7 o r 20.$

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