Question

Which equations have the same pair of solutions?

a) (1+6) (2-6)=0
b) (2+6) (x+6) = 0
c) (z - 6) (1 - 6) = 0
d) (2x +12) (2x - 12) = 0

Answer 1

Equations (b) and (d) have the same pair of solutions, which are x = 6 and x = -6, determined by the zero-product property.

Step-by-step explanation:

The question is asking which of the given equations have the same pair of solutions. To determine this, we need to put the equations into a comparable form and solve them if necessary. Let's analyze the given options:

• Equation (a): (1+6) (2-6)=0 becomes 7(-4)=0 which is not a true statement, so it does not represent an equation with solutions.
• Equation (b): (2+6) (x+6) = 0 simplifies to 8(x+6)=0. This yields one solution x = -6.
• Equation (c): (z - 6) (1 - 6) = 0 simplifies to (z - 6)(-5)=0 yielding one solution z = 6.
• Equation (d): (2x+12)(2x-12)=0 is a difference of squares that equates to (2x)^2 - 12^2=0. The solutions are x = 6 and x = -6.

Among the equations, only (b) and (d) yield the same pair of solutions which are x = -6 and x = 6, based on the zero-product property (if ab = 0, then either a = 0 or b = 0 or both).