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Zorluk: KolayQuadratic 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 = -2Cevap
  3. C
    x=6x = 6 and x=2x = 2
  4. D
    x=−6x = -6 and x=−2x = -2

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

Solving quadratic equations by factoring
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Konular

Quadratic Equations

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