Which of the following numbers does b have to be divisible by for the equation ax^2 + bx + c = 0 to have equal roots: 3, 4, 5, 6?

The roots of a quadratic equation ax^2 + bx + c = 0 can be
expressed as [-b + sqrt (b^2 – 4ac)]/2a and [-b - sqrt (b^2 –
4ac)]/2a.

If the two roots have to be equal b^2 – 4ac
should be equal to 0.

Equating b^2 – 4ac to
0

=> b^2 =
4ac

=> b has to be a multiple of
4.

Therefore for a quadratic equation ax^2 +
bx + c = 0 to have equal roots the coefficient b has to be a multiple of 4, irrespective
of the value of a and c.