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Is the given equation a quadratic equation? Explain.

3(x-6)

1. The equation is not a quadratic equation because the expression is not set to zero.
2. The equation is a quadratic equation because there is an x term.
3. The equation is not a quadratic equation because there is no x term.
4. The equation is not a quadratic equation because there is a term with a degree higher than 2.

User Emre Bener
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1 Answer

5 votes

Final answer:

The given expression 3(x-6) + 1 is not a quadratic equation because it simplifies to a linear equation 3x - 17, lacking the characteristic x² term required for quadratic equations. Option 4 is correct.

Step-by-step explanation:

To determine whether the given expression 3(x-6) + 1 is a quadratic equation, we need to assess if it can be rewritten in the standard form of a quadratic, which is ax² + bx + c = 0. Starting with 3(x-6) + 1, when we expand this, we get 3x - 18 + 1.

Simplifying further, we get 3x - 17, which is a linear equation since it is in the form of ax + b = 0, where 'a' and 'b' are constants and there is no x² term present. Therefore, the correct answer is that the equation is not a quadratic equation because there is no x² term, which makes the first given statement incorrect.

Quadratic equations are mathematical functions known as second-order polynomials and have the characteristic x² term. The absence of this x² term in our original expression indicates that it cannot be a quadratic equation.

The given equation 3(x-6) 1 is not a quadratic equation.

A quadratic equation is an equation of the form ax²+bx+c = 0, where the highest power of x is 2. In the given equation, there is no x² term or any term with a degree higher than 2. Thus, it is not a quadratic equation.

Therefore, option 4: The equation is not a quadratic equation because there is a term with a degree higher than 2 is the correct choice.

User Rafael Angarita
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