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[tex]9a^2 + 10a + 1 =[/tex]
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Response:
Complete the equation:
[tex]\[ 9a^2 + 10a + 1 = \][/tex]

Sagot :

GinnyAnswer
Certainly! Let's break down the expression [tex]\(9a^2 + 10a + 1\)[/tex] step by step.

### Understanding the Expression

We have a quadratic expression:

[tex]\[ 9a^2 + 10a + 1 \][/tex]

This is already in its simplified form. To understand it better, let's identify the components:

1. Coefficients:
- The coefficient of [tex]\(a^2\)[/tex] is 9.
- The coefficient of [tex]\(a\)[/tex] is 10.
- The constant term is 1.

2. Standard Form:
- This expression is in the standard quadratic form [tex]\( ax^2 + bx + c \)[/tex], where:
- [tex]\(a = 9\)[/tex]
- [tex]\(b = 10\)[/tex]
- [tex]\(c = 1\)[/tex]

### Detailed Examination

#### 1. Quadratic Term ([tex]\(9a^2\)[/tex]):
- This term represents the portion of the expression that changes with the square of [tex]\(a\)[/tex]. The higher the value of [tex]\(a\)[/tex], the more rapidly [tex]\(9a^2\)[/tex] will increase since it grows proportionally to [tex]\(a^2\)[/tex].

#### 2. Linear Term ([tex]\(10a\)[/tex]):
- This term changes linearly with [tex]\(a\)[/tex]. Each unit increase in [tex]\(a\)[/tex] adds 10 to the value of the expression.

#### 3. Constant Term (1):
- This term does not change with [tex]\(a\)[/tex]; it simply adds 1 to the overall value of the expression.

### Importance of the Expression

- Graph Representation: The graph of this quadratic expression will be a parabola facing upwards since the coefficient of [tex]\(a^2\)[/tex] (which is 9) is positive.
- Roots/Solutions: To find the roots of the quadratic expression, one typically sets the expression equal to zero and solves for [tex]\(a\)[/tex]. For this specific expression, you would solve the equation [tex]\(9a^2 + 10a + 1 = 0\)[/tex] using methods such as factoring, completing the square, or using the quadratic formula.

### Conclusion

The given quadratic expression is in its simplest form and comprises three terms: a quadratic term [tex]\(9a^2\)[/tex], a linear term [tex]\(10a\)[/tex], and a constant term 1. The expression does not need any further simplification.

So,

[tex]\[ 9a^2 + 10a + 1 \][/tex]

is the detailed form of the quadratic expression.
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