Tell whether it is a quadratic Equation or not 3x + 8 = 15) E @x² + 5x-7=0 2 ③ 12 Ex-4)=0) ④ 2x²-7x = 12, ⑤ (x=47(x+6) = 0

To determine whether the given equations are quadratic equations, we need to check if they can be written in the standard form of a quadratic equation:

\[ ax^2 + bx + c = 0 \]

Where \( a \), \( b \), and \( c \) are constants, and \( a \neq 0 \).

Let's examine each equation:

1. \( 3x + 8 = 15 \)

Subtract 15 from both sides:

\[ 3x + 8 - 15 = 0 \]
\[ 3x - 7 = 0 \]

This equation is linear, not quadratic, because it doesn't have an \( x^2 \) term.

2. \( x^2 + 5x - 7 = 0 \)

This is already in the standard form of a quadratic equation.

3. \( 12 \cdot (x - 4) = 0 \)

Expand the equation:

\[ 12x - 48 = 0 \]

This equation is linear, not quadratic, because it doesn't have an \( x^2 \) term.

4. \( 2x^2 - 7x = 12 \)

Subtract 12 from both sides:

\[ 2x^2 - 7x - 12 = 0 \]

This is in the standard form of a quadratic equation.

5. \( (x - 4)(x + 6) = 0 \)

Expand the equation:

\[ x^2 + 6x - 4x - 24 = 0 \]
\[ x^2 + 2x - 24 = 0 \]

This is in the standard form of a quadratic equation.

### Summary:

1. \( 3x + 8 = 15 \) - Not a quadratic equation (linear).
2. \( x^2 + 5x - 7 = 0 \) - Quadratic equation.
3. \( 12 \cdot (x - 4) = 0 \) - Not a quadratic equation (linear).
4. \( 2x^2 - 7x = 12 \) - Quadratic equation.
5. \( (x - 4)(x + 6) = 0 \) - Quadratic equation.

Would you like more details or have any questions about these classifications?

Here are 8 related questions:
1. What defines a quadratic equation?
2. How can we solve quadratic equations?
3. What are the different methods to factor quadratic equations?
4. How can the quadratic formula be used to solve quadratic equations?
5. What are the properties of the roots of quadratic equations?
6. How can we graph quadratic equations?
7. What is the significance of the discriminant in a quadratic equation?
8. How do we complete the square to solve a quadratic equation?

Tip: Always ensure an equation fits the \( ax^2 + bx + c = 0 \) form to confirm it is quadratic.

Learn how to identify quadratic equations through examples and explanations. This page covers the differences between quadratic and linear equations using specific examples like 3x + 8 = 15 and x^2 + 5x - 7 = 0. Suitable for students in Grades 7-9.

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