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Kx^2-16x+32=0

Solve for k if the roots of the equation kx^2-16x+32=0 are equal.

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John M. | Analytical assistance -- Writing, Math, and moreAnalytical assistance -- Writing, Math, ...
4.8 4.8 (154 lesson ratings) (154)
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Mol, for the roots to be equal their factored equations have to be the same, i.e. in the form of (ax+b)^2=0 or a^2x^2 + 2abx + b^2 = 0, so if we replace the numbers in front of the x terms in the given equation with the coefficients above, we'll get 3 equations:
 
a^2=k,
2ab=-16, and
b^2=32, so b=±4√2,
so a=±2/√2=±√2
and (±√2)^2=2=k
 
For a final equation of 2x^2+16x+32=0
Deanna L. | Electrical engineering major and music lover with MIT degreeElectrical engineering major and music l...
4.9 4.9 (120 lesson ratings) (120)
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UsingUsing the quadratic root equation we see that a is k, b is -16, and c is 32. If the roots are equal they are -b/2a making b^2-4ac zero ( you can look up the full formula if you are curious) or 256=128k. So k is 2 (it would have two imaginary roots if b^2-4ac were negative and two different roots if the term were positive ).