Examkin

Question

Difficulty: EasyQuadratic Equations

What are the solutions to the quadratic equation x2−4x−12=0x^2 - 4x - 12 = 0?

  1. A
    x=−6x = -6 and x=2x = 2
  2. x=6x = 6 and x=−2x = -2Answer
  3. C
    x=6x = 6 and x=2x = 2
  4. D
    x=−6x = -6 and x=−2x = -2

Answer

The solutions are x=6x = 6 and x=−2x = -2.
The correct answer is x=6x = 6 and x=−2x = -2. Factoring the quadratic equation x2−4x−12=0x^2 - 4x - 12 = 0 involves finding two numbers whose product is −12-12 and whose sum is −4-4. These numbers are −6-6 and 22. Rewriting the equation as (x−6)(x+2)=0(x - 6)(x + 2) = 0 and setting each factor to zero yields the solutions x=6x = 6 and x=−2x = -2.

Step-by-Step Solution

1
Identify the quadratic equation to factor.
The equation is x2−4x−12=0x^2 - 4x - 12 = 0.
To find the solutions, we need to rewrite the quadratic expression in factored form.
2
Find two numbers that multiply to −12-12 and add up to −4-4.
The numbers are −6-6 and 22.
These numbers satisfy both conditions: (−6)×2=−12(-6) \times 2 = -12 and −6+2=−4-6 + 2 = -4.
3
Write the quadratic equation in factored form and solve for xx.
(x−6)(x+2)=0(x - 6)(x + 2) = 0, which means x−6=0x - 6 = 0 or x+2=0x + 2 = 0. Thus, x=6x = 6 or x=−2x = -2.
Applying the zero product property allows us to solve for the individual values of xx.

Key Concept

Solving quadratic equations by factoring
Rate this question

Topics

Quadratic Equations

More questions from this topic