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