The quadratic equation x^2 - 4x - 12 = 0 has two real solutions. What is the value of the … — ACT

The quadratic equation $x^2 - 4x - 12 = 0$ has two real solutions. What is the value of the positive solution to this equation?

Answer: 6

The positive solution to the equation is

6

Factoring the quadratic trinomial

x^2 - 4x - 12 = 0

yields

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

. Setting the individual binomial factors to zero gives the solutions

x = 6

and

x = -2

. The positive solution among these is

6

Factor the quadratic equation

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

Factoring the trinomial

x^2 - 4x - 12

requires finding two integers whose product is

-12

and whose sum is

-4

. These numbers are

-6

and

2

Apply the zero product property

x - 6 = 0

x + 2 = 0

If the product of two factors is equal to zero, then at least one of the individual factors must equal zero.

Solve for the variable and identify the positive root

x = 6

and

x = -2

Solving the linear equations yields

x = 6

and

x = -2

. Since the question asks for the positive solution, we select

6

Solving quadratic equations by factoring

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