Solution: Find the value of $k$ such that $x^2 + kx + 9$ has exactly one real root.

Code:

import sympy

x, k = sympy.symbols('x k')
# A quadratic ax^2 + bx + c has exactly one real root if its discriminant b^2 - 4ac is zero.
# For x^2 + kx + 9: a=1, b=k, c=9
discriminant = k**2 - 4*1*9
solutions = sympy.solve(discriminant, k)

print(f"{discriminant=}")
print(f"{solutions=}")

Output:

discriminant=k**2 - 36
solutions=[-6, 6]