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5. Which is a quadratic inequality?

A. [tex] x^2 + 5x + 10 \ \textgreater \ 25 [/tex]
B. [tex] 5x^2 + 3x + 12 = 0 [/tex]
C. [tex] x^3 + 12 \ \textless \ -3 [/tex]
D. [tex] 3x + 7 \ \textgreater \ 12 [/tex]

Sagot :

GinnyAnsweridn
To determine which of the given options is a quadratic inequality, let's review the characteristics of each:

1. Quadratic inequality: A quadratic inequality involves a quadratic expression (a polynomial of degree 2) where the inequality symbol (>, <, ≥, ≤) is used instead of the equality symbol (=).

2. Option 1: \(x^2 + 5x + 10 > 25\)
- This is a quadratic expression, \(x^2 + 5x + 10\), set greater than 25.
- Since it involves a polynomial of degree \(2\) and uses the '>' inequality symbol, this is a quadratic inequality.

3. Option 2: \(5x^2 + 3x + 12 = 0\)
- This is a quadratic equation because it involves a polynomial of degree \(2\) and an equality symbol.

4. Option 3: \(x^3 + 12 < -3\)
- This is a cubic inequality because it involves a polynomial of degree \(3\) and an inequality symbol.

5. Option 4: \(3x + 7 > 12\)
- This is a linear inequality because it involves a linear polynomial (degree \(1\)) and an inequality symbol.

Thus, given the examination of each option, the one that fulfills the criteria of a quadratic inequality is:

[tex]\[ x^2 + 5x + 10 > 25 \][/tex]

Hence, the correct answer is:

Option 1: [tex]\( x^2 + 5x + 10 > 25 \)[/tex]
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