The equation x^2 -3x +k^2 = 4 has two distinct real roots. Find the possible values of k.

Question

How do I do this?? I know the basics of solving equations like these put this one's got me fooled.

Answer 1

The equation has two distinct real roots when the discriminant, b^2 - 4ac > 0.

x^2 - 3x + k^2 - 4 = 0

a = 1, b = -3, c = k^2 - 4

(-3)^2 - 4(1)(k^2 - 4) > 0

9 - 4k^2 + 16 > 0

-4k^2 > -25 When you divide both sides of a inequality bu a negative number, the inequality sign reverses.

k^2 < 25/4 Take the square root of both sides.

k < 5/2