Math Problem Statement

x^2-(4*x)-5

Solution

The expression you have is:

x24x5x^2 - 4x - 5

To solve for the roots of this quadratic equation, we can factor it. We are looking for two numbers that multiply to -5 and add up to -4. The numbers are -5 and +1. So we can factor the expression as:

(x5)(x+1)=0(x - 5)(x + 1) = 0

Setting each factor equal to zero:

x5=0orx+1=0x - 5 = 0 \quad \text{or} \quad x + 1 = 0

Solving these gives:

x=5orx=1x = 5 \quad \text{or} \quad x = -1

So, the roots of the equation x24x5=0x^2 - 4x - 5 = 0 are x=5x = 5 and x=1x = -1.

Would you like more details on the solution, or do you have any questions?


Here are 5 related questions you might find interesting:

  1. How can you verify the roots of a quadratic equation using the quadratic formula?
  2. What is the discriminant of the equation x24x5=0x^2 - 4x - 5 = 0?
  3. How do you graph a quadratic equation like x24x5x^2 - 4x - 5?
  4. What does the vertex of the quadratic equation x24x5x^2 - 4x - 5 represent geometrically?
  5. How do you solve a quadratic equation by completing the square?

Tip: Always check if the quadratic can be factored before jumping to the quadratic formula—it might save you time!

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Factoring

Formulas

Factoring quadratic equations
Zero Product Property

Theorems

Factorization method
Zero Product Property

Suitable Grade Level

Grades 7-9