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Sagot :
Sure! Let's determine if each given equation is quadratic.
### 1. [tex]\( 3x + 8 = 15 \)[/tex]
First, we'll rearrange the equation to standard form:
[tex]\[ 3x + 8 - 15 = 0 \][/tex]
[tex]\[ 3x - 7 = 0 \][/tex]
This equation simplifies to:
[tex]\[ 3x = 7 \][/tex]
This is a linear equation, not a quadratic one.
Conclusion: This is not a quadratic equation.
### 2. [tex]\( x^2 - 5x + 10 = 0 \)[/tex]
The equation is already in standard form [tex]\( ax^2 + bx + c = 0 \)[/tex], where [tex]\( a = 1 \)[/tex], [tex]\( b = -5 \)[/tex], and [tex]\( c = 10 \)[/tex].
Since [tex]\( a \neq 0 \)[/tex] (here [tex]\( a = 1 \)[/tex]), this is a quadratic equation.
Conclusion: This is a quadratic equation.
### 3. [tex]\( 12 - 4x = 0 \)[/tex]
First, rearrange the equation to standard form:
[tex]\[ -4x + 12 = 0 \][/tex]
[tex]\[ -4x = -12 \][/tex]
This equation simplifies to:
[tex]\[ x = 3 \][/tex]
This is a linear equation, not a quadratic one.
Conclusion: This is not a quadratic equation.
### 4. [tex]\( 2x^2 - 7x = 12 \)[/tex]
First, we'll rearrange the equation to standard form:
[tex]\[ 2x^2 - 7x - 12 = 0 \][/tex]
The equation is now in standard form [tex]\( ax^2 + bx + c = 0 \)[/tex], where [tex]\( a = 2 \)[/tex], [tex]\( b = -7 \)[/tex], and [tex]\( c = -12 \)[/tex].
Since [tex]\( a \neq 0 \)[/tex] (here [tex]\( a = 2 \)[/tex]), this is a quadratic equation.
Conclusion: This is a quadratic equation.
### 5. [tex]\( 6 - 2x + 3x^2 = 0 \)[/tex]
The equation is already in standard form [tex]\( ax^2 + bx + c = 0 \)[/tex], where [tex]\( a = 3 \)[/tex], [tex]\( b = -2 \)[/tex], and [tex]\( c = 6 \)[/tex].
Since [tex]\( a \neq 0 \)[/tex] (here [tex]\( a = 3 \)[/tex]), this is a quadratic equation.
Conclusion: This is a quadratic equation.
### Summary:
1. [tex]\( 3x + 8 = 15 \)[/tex] → Not quadratic
2. [tex]\( x^2 - 5x + 10 = 0 \)[/tex] → Quadratic
3. [tex]\( 12 - 4x = 0 \)[/tex] → Not quadratic
4. [tex]\( 2x^2 - 7x = 12 \)[/tex] → Quadratic
5. [tex]\( 6 - 2x + 3x^2 = 0 \)[/tex] → Quadratic
Hence, the equations (i), (iii) are not quadratic, while equations (ii), (iv), and (v) are quadratic.
### 1. [tex]\( 3x + 8 = 15 \)[/tex]
First, we'll rearrange the equation to standard form:
[tex]\[ 3x + 8 - 15 = 0 \][/tex]
[tex]\[ 3x - 7 = 0 \][/tex]
This equation simplifies to:
[tex]\[ 3x = 7 \][/tex]
This is a linear equation, not a quadratic one.
Conclusion: This is not a quadratic equation.
### 2. [tex]\( x^2 - 5x + 10 = 0 \)[/tex]
The equation is already in standard form [tex]\( ax^2 + bx + c = 0 \)[/tex], where [tex]\( a = 1 \)[/tex], [tex]\( b = -5 \)[/tex], and [tex]\( c = 10 \)[/tex].
Since [tex]\( a \neq 0 \)[/tex] (here [tex]\( a = 1 \)[/tex]), this is a quadratic equation.
Conclusion: This is a quadratic equation.
### 3. [tex]\( 12 - 4x = 0 \)[/tex]
First, rearrange the equation to standard form:
[tex]\[ -4x + 12 = 0 \][/tex]
[tex]\[ -4x = -12 \][/tex]
This equation simplifies to:
[tex]\[ x = 3 \][/tex]
This is a linear equation, not a quadratic one.
Conclusion: This is not a quadratic equation.
### 4. [tex]\( 2x^2 - 7x = 12 \)[/tex]
First, we'll rearrange the equation to standard form:
[tex]\[ 2x^2 - 7x - 12 = 0 \][/tex]
The equation is now in standard form [tex]\( ax^2 + bx + c = 0 \)[/tex], where [tex]\( a = 2 \)[/tex], [tex]\( b = -7 \)[/tex], and [tex]\( c = -12 \)[/tex].
Since [tex]\( a \neq 0 \)[/tex] (here [tex]\( a = 2 \)[/tex]), this is a quadratic equation.
Conclusion: This is a quadratic equation.
### 5. [tex]\( 6 - 2x + 3x^2 = 0 \)[/tex]
The equation is already in standard form [tex]\( ax^2 + bx + c = 0 \)[/tex], where [tex]\( a = 3 \)[/tex], [tex]\( b = -2 \)[/tex], and [tex]\( c = 6 \)[/tex].
Since [tex]\( a \neq 0 \)[/tex] (here [tex]\( a = 3 \)[/tex]), this is a quadratic equation.
Conclusion: This is a quadratic equation.
### Summary:
1. [tex]\( 3x + 8 = 15 \)[/tex] → Not quadratic
2. [tex]\( x^2 - 5x + 10 = 0 \)[/tex] → Quadratic
3. [tex]\( 12 - 4x = 0 \)[/tex] → Not quadratic
4. [tex]\( 2x^2 - 7x = 12 \)[/tex] → Quadratic
5. [tex]\( 6 - 2x + 3x^2 = 0 \)[/tex] → Quadratic
Hence, the equations (i), (iii) are not quadratic, while equations (ii), (iv), and (v) are quadratic.
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