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for what value(s) of m will the equation have = roots (3m +

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Director
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for what value(s) of m will the equation have = roots (3m + [#permalink] New post 10 Jan 2005, 15:27
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for what value(s) of m will the equation have = roots

(3m + 1) X^2 + 2(m+1)X + m = 0
Intern
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 [#permalink] New post 10 Jan 2005, 16:04
hmm " = roots " .. u mean have equal roots ? or is it that the equation will have non imaginary roots ...

I think if we take it as equal roots..
then m = -1/2 and 1
Director
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 [#permalink] New post 10 Jan 2005, 16:09
i meant equal roots and your answer is correct
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 [#permalink] New post 11 Jan 2005, 22:01
maybe i am not undestanding the quesiton, but can any of you guys explain the answer. are there any answer choices ???
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 [#permalink] New post 11 Jan 2005, 23:07
Good question. m = 1.

suppose m=1 and replace m with 1 in the given eq,

4X^2 + 4X + 1 = 0

solving the eq, x = -1/2 or roots of the eq is -1/2.
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 [#permalink] New post 11 Jan 2005, 23:17
(3m + 1) X^2 + 2(m+1)X + m = 0
is a quadratic equation of form aX^2 + bX + c

The roots of this equation are equal if b^2 - 4*a*c = 0

=> Roots are equal if (2(m+1))^2 - 4*(3m+1)(m) = 0

Solve for m , you get the answers
  [#permalink] 11 Jan 2005, 23:17
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for what value(s) of m will the equation have = roots (3m +

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