Question

Write ""Fact"" if the equation is quadratic and ""Bluff"" if the equation is not quadratic.

1. x^2 + x - 3 = 0
Answer:
2. x^2 = 2x (6x^2 + 4)
Answer:
3. 2x^2 = 7%
Answer:

Please provide your answers for each equation by indicating whether it is a quadratic equation (Fact) or not (Bluff).

Answer 1

The equation x² + x - 3 = 0 is a quadratic equation (Fact), while x² = 2x (6x² + 4) is not a quadratic equation (Bluff). The equation 2x² = 7% is a quadratic equation (Fact) after converting 7% into a decimal.

Step-by-step explanation:

To determine whether a given equation is a quadratic equation, we need to check if it can be represented in the standard form ax² + bx + c = 0, where a, b, and c are constants and 'a' is not zero. A quadratic equation has the highest power of x as 2.

1. x² + x - 3 = 0
   Answer: Fact. This equation is already in the standard form ax² + bx + c = 0 where a = 1, b = 1, and c = -3.
2. x² = 2x (6x² + 4)
   Answer: Bluff. If we try to simplify this, it becomes x² = 12x³ + 8x, which is clearly not a quadratic equation as the highest power of x is 3.
3. 2x² = 7%
   Answer: Fact. First, convert 7% to a decimal (

To solve these quadratic equations, one would use the quadratic formula which is x = (-b ± √(b²-4ac))/(2a), where the discriminant (b²-4ac) determines the nature and number of roots.