Multiple choice

Which of the following equations when simplified will be a Quadratic Equation?

  1. $(x+3)(x-7)= x^2-8x$
  2. $(x+1) (2x+1)=x^2+x+9$
  3. $(x+2)^2 = x^2 + 1$

  4. None of these.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A quadratic equation must have an x^2 term after simplification. Option B: (x+1)(2x+1) = 2x^2 + 3x + 1. 2x^2 + 3x + 1 = x^2 + x + 9 leads to x^2 + 2x - 8 = 0, which is quadratic.

AI explanation

For an equation to be quadratic, the highest power of the variable x must be exactly 2 after simplification. In option B, expanding the product (x+1)(2x+1) yields 2x^2 + 3x + 1. Subtracting x^2 + x + 9 from both sides results in x^2 + 2x - 8 = 0, which is a valid quadratic equation. The required answer is x^2 + 2x - 8 = 0.

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