If x > 0 and x^2 - 6x - 16 = 0, what is the value of x? — GRE General Test

If $x > 0$ and $x^2 - 6x - 16 = 0$ , what is the value of $x$ ?

Answer: 8

The correct value of

x

is 8.

Factoring

x^2 - 6x - 16 = 0

gives

(x - 8)(x + 2) = 0

. Setting each factor to zero yields

x = 8

and

x = -2

. Given the constraint

x > 0

, the only valid answer is 8.

Factor the quadratic expression

(x - 8)(x + 2) = 0

Find two numbers that multiply to

-16

and add to

-6

, which are

-8

and

2

Solve for possible values of

x

x = 8

x = -2

By the zero-product property, if

(x - 8)(x + 2) = 0

, then either

x - 8 = 0

x + 2 = 0

Apply the given constraint

x > 0

x = 8

The solution

x = -2

is rejected because

x

must be positive.

Factoring Quadratic Equations

Estimated Time:45s

Question