Question

Determine wether the following are equations are QUADRATIC or NOT:

1.) 2x²(x²-1)=0
2.)2x²-x=4
3.)3x-5x=4
4.)½x²+x=1
5.)x(x-6)=10

Answer 1

The expressions given are examined and classified based on the presence of an x-squared term. Three of them are quadratic equations as they have a term with x raised to the second power, while one is not because it simplifies to a linear equation.

Step-by-step explanation:

To determine whether the given expressions are quadratic or not, we remember that a quadratic equation is of the form ax2 + bx + c = 0, where a, b, and c are constants, and a is not equal to zero.

1. 2x2(x2 - 1) = 0: Yes, this is a quadratic equation because it can be expanded to 2x4 - 2x2 = 0, which has a term with x raised to the second power.
2. 2x2 - x = 4: Yes, this is a quadratic equation because it is already in the standard form with a = 2, b = -1, and c = -4.
3. 3x - 5x = 4: No, this is not a quadratic equation. It simplifies to -2x = 4, which is linear.
4. 1/2x2 + x = 1: Yes, this is a quadratic equation because it has the x-squared term.
5. x(x - 6) = 10: Yes, this is a quadratic equation when expanded; it becomes x2 - 6x - 10 = 0.