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Given the quadratic equation kx² + 2x + 4 = 0, find the value of k so that the roots are equal.

How do I do this?

The "quadratic equation" to solve ax^2 + bx + c = 0:
x = (-b +/- sqrt(b^2 - 4*a*c*))/2*a

gives two values of x exactly when
(b^2 - 4*a*c*) > 0

one value of x exactly when
(b^2 - 4*a*c*) = 0

and no (real) values of x exactly when
(b^2 - 4*a*c*) < 0

hence you want (b^2 - 4*a*c*) = 0
substitute in b=2, a=k, c=4 and you're away.