(x-1)(x+3)=0 Find The Roots Of Equation

2 min read Jun 17, 2024
(x-1)(x+3)=0 Find The Roots Of Equation

Solving the Equation (x-1)(x+3) = 0

This equation is already in factored form, making it very easy to find the roots.

Understanding the Zero Product Property

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

In our equation, we have two factors: (x-1) and (x+3). For the product to equal zero, one or both of these factors must equal zero.

Finding the Roots

Let's set each factor equal to zero and solve for x:

  • Factor 1: (x-1) = 0
    • Add 1 to both sides: x = 1
  • Factor 2: (x+3) = 0
    • Subtract 3 from both sides: x = -3

Therefore, the roots of the equation (x-1)(x+3) = 0 are x = 1 and x = -3.

Verification

We can verify these roots by plugging them back into the original equation:

  • For x = 1: (1-1)(1+3) = 0 * 4 = 0 (True)
  • For x = -3: (-3-1)(-3+3) = -4 * 0 = 0 (True)

This confirms that our solutions are correct.

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