How many positive integer values of x satisfy the quadratic inequality x^2 - 4x - 5 < 0? — JAMB UTME

How many positive integer values of $x$ satisfy the quadratic inequality $x^2 - 4x - 5 < 0$ ?

Answer: 4

There are 4 positive integer values of

x

that satisfy the inequality.

Factoring

x^2 - 4x - 5 < 0

yields

(x - 5)(x + 1) < 0

, giving the real solution interval

-1 < x < 5

. Filtering for positive integers (

x \in \mathbb{Z}^+

) yields the set

\{1, 2, 3, 4\}

, which contains exactly 4 values.

Factor the quadratic inequality

(x - 5)(x + 1) < 0

Factoring helps find the boundary roots of the quadratic equation.

Determine the solution set interval

-1 < x < 5

For a quadratic inequality of the form

(x - a)(x - b) < 0

with

a < b

, the solution interval is

a < x < b

List the positive integer solutions in the range

-1 < x < 5

x \in \{1, 2, 3, 4\}

Positive integers are whole numbers strictly greater than 0.

Count the number of positive integers

Counting the elements in the set

\{1, 2, 3, 4\}

gives a total of 4.

Solving quadratic inequalities and finding valid integer solutions within a target domain.

Estimated Time:45s

Question