The only situation where the quadratic formula cannot be used is B. The coefficient of the x-term is zero. This makes the equation linear, not quadratic.
The quadratic formula only applies to quadratic equations, which are defined as polynomial equations of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. Therefore, let's analyze each option:
A. The coefficient of the x²-term is 1: This is a valid situation for using the quadratic formula. The value of the coefficient a doesn't affect the applicability of the formula as long as it's not zero.
B. The coefficient of the x-term is zero: This actually makes the equation linear, not quadratic. Linear equations have a different method of solution and cannot be solved using the quadratic formula. So, this is the situation where the formula won't work.
C. The degree of the polynomial expression is 2: This is a valid situation. By definition, a quadratic equation has a degree of 2.
D. The right-hand side of the equation is 1: The right-hand side (c) doesn't affect the applicability of the quadratic formula as long as the equation is in the form ax² + bx + c = 0.