If x is a solution to the quadratic equation x^2 - 11x + 28 = 0 such that x > 5, what is t… — GRE General Test

If $x$ is a solution to the quadratic equation $x^2 - 11x + 28 = 0$ such that $x > 5$ , what is the value of $x$ ?

Answer: 7

The value of

x

is 7.

Factoring

x^2 - 11x + 28 = 0

yields

(x - 7)(x - 4) = 0

, giving solutions

x = 7

and

x = 4

. Since the problem specifies that

x > 5

, the only valid value for

x

is 7.

Factor the quadratic expression

(x - 7)(x - 4) = 0

Find two numbers that multiply to 28 and sum to -11, which are -7 and -4.

Find the roots of the equation

x = 7

x = 4

Set each linear factor equal to 0 and solve for

x

Apply the given constraint

x > 5

x = 7

Out of the two roots 4 and 7, only 7 is strictly greater than 5.

Factoring quadratic equations of the form

x^2 + bx + c = 0

Question