Question

Find all values of n such that x^2 + bx + (b/2)^2 = n has
a. one real root. b. two real roots. c. two imaginary roots.

Answer 1

\[x ^{2} + bx + (b/2)^{2} = n\]

Answer 2

Write this as a quadratic equation
\[ x^2 + bx + (b^2/4 - n) = 0 \]
Now evaluate the discriminant, call it \( d \).

If d > 0, then the quadratic has two real roots
If d = 0, then the quadratic has one real root
If d < 0, then the quadratic has no real roots