(x^2-6)(x^2+1)=0

Jasonbradley

2 min read

·

Jun 17, 2024

16

Share

Solving the Equation (x^2 - 6)(x^2 + 1) = 0

This equation represents a quartic equation, meaning it has a highest power of 4. To solve it, we can use the Zero Product Property: If the product of two or more factors is zero, then at least one of the factors must be zero.

Here's how to solve the equation:

1. Set each factor to zero:

   • x² - 6 = 0
   • x² + 1 = 0

2. Solve for x in each equation:

   • For x² - 6 = 0:
     • Add 6 to both sides: x² = 6
     • Take the square root of both sides: x = ±√6
   • For x² + 1 = 0:
     • Subtract 1 from both sides: x² = -1
     • Take the square root of both sides: x = ±√(-1)
     • Since the square root of a negative number is imaginary, we express it as x = ±i

Therefore, the solutions to the equation (x² - 6)(x² + 1) = 0 are:

• x = √6
• x = -√6
• x = i
• x = -i

Key points to remember:

• The Zero Product Property is a powerful tool for solving equations where the product of factors equals zero.
• When taking the square root of both sides of an equation, remember to consider both positive and negative solutions.
• The square root of a negative number is an imaginary number, represented by 'i'.