Question

if x=2 and x=3 are roots of the equation 3x2-2kx +2m = 0,find the value of k and m

Answer 1

Solution :

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Given :

 2 & 3 are the roots of the equation, 3x² - 2kx + 2m = 0.

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To Find :

The value of k & m

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If x = 2,

We get,

⇒ 3x² - 2kx + 2m = 0

⇒ 3(2)² - 2k(2) + 2m = 0

⇒ 3(4) - 4k + 2m = 0.

⇒ 12 - 4k + 2m = 0

⇒ -4k + 2m = -12

⇒ 2k - m = 6 ....(i)

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If x = 3,

Then,

⇒ 3x² - 2kx + 2m = 0

⇒ 3(3)² - 2k(3) + 2m = 0

⇒ 3(9) - 6k + 2m = 0

⇒ 27 - 6k + 2m = 0

⇒ -6k + 2m = -27

⇒ 3k - m = 13. 5..(ii)

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Subtracting equation (i) from (ii),

We get,

⇒ (3k - m) - (2k - m) = 13.5 - 6

⇒ 3k - m - 2k + m = 7.5

⇒ ∴ k = 7.5

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Substituting value of x in (i),

We get,

⇒ 2k - m = 6

⇒ 2(7.5) - m = 6

⇒ 15 - m = 6

⇒ -m = 6 - 15

⇒ -m = -9

⇒ ∴ m = 9

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                                           Hope it Helps !!

Answer 2

Hence the ans is k =15/2 where as m=9