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ZERO-PRODUCT PROPERTY

Definition of Zero-Product Property

If the product of two or more factors is zero then at least one of the factors should be zero. This property is known as Zero-Product Property.

That is, if XY = 0, then X = 0 or Y = 0 or both X and Y are equal to 0.
Similarly, if XYZ = 0, then X = 0 or Y = 0 or Z = 0 or all three are 0.
This thought can be extended to any number of factors.

More About Zero-Product Property

The x-coordinate of the point where a line intersects the y-axis is 0. So, the y-intercept of a line can also be found by substituting x = 0 in the equation of the line.

Examples of Zero-Product Property

Ques: Consider this simple algebra problem. Solve x2 -4x = 0.

Solution:

Let's solve this equation through factoring, followed by the application of the Zero-Product Property
x2-4x = 0 ⇒ x (4 - x) = 0 [Taking out the common variable x]
⇒ x = 0 or (4 - x) = 0 [Recall the definition of Zero-product Property.]
⇒ x = 0 or x = 4
So, the solutions are x = 0 or x = 4
Both these values satisfy the original equation x2 - 4x = 0


Video Examples: The Zero-Product Property


Solved Example on Zero-Product Property

Ques: Solve for x: x2 + 4x - 5 = 0

Solution:

  • x2 + 4x - 5 = 0
    ⇒ x2 + 5x - x - 5 = 0 [Splitting the middle term]
  • ⇒ x(x + 5) - 1(x+5) = 0 [Taking out the common factors]
  • (x + 5)(x - 1) = 0 [Factor.]
  • ⇒ x + 5 = 0 or (x - 1) = 0 [Recall the definition of Zero-product property.]
  • ⇒ x = -5 or x = 1
  • So, the solutions are x = -5 or x = 1
  • Both these values satisfy the original equation x2 + 4x - 5 = 0.

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