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若关于

x

的不等式

x^{2}-\left(m+\frac{5}{2}\right) x+2 m<0

的解集中恰有 2 个整数，则实数

m

的取值...

Mar 8, 2024

若关于

x

的不等式 x^{2}-\left(m+\frac{5}{2}\right) x+2 m<0 的解集中恰有 2 个整数，则实数

m

的取值范围为

Solution by Steps

step 1

Identify the quadratic inequality to solve: x^2 - \left(m + \frac{5}{2}\right)x + 2m < 0

step 2

Factor the quadratic inequality if possible

step 3

Determine the critical points by setting the factors equal to zero

step 4

Analyze the intervals determined by the critical points to find where the inequality is satisfied

step 5

Since the solution set must contain exactly 2 integers, adjust the value of

m

to satisfy this condition

Answer

The range of

m

for which the solution set of the inequality x^2 - \left(m + \frac{5}{2}\right)x + 2m < 0 contains exactly 2 integers is not provided by the asksia-ll calculator result.

Key Concept

Quadratic Inequalities

Explanation

To solve a quadratic inequality, one must find the values of

x

for which the quadratic expression is less than zero. The solution set is determined by the intervals between the roots of the corresponding quadratic equation. The number of integers in the solution set depends on the distance between these roots and their location on the number line.