Kx^2-16x+32=0

Question

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

Answer 1

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 ).

Answer 2

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