Multiple choice

Is the following equation a quadratic equation? $16x^2 - 3 = (2x + 5) (5x - 3)$

  1. Yes

  2. No

  3. Ambiguous

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Expanding the right side: (2x + 5)(5x - 3) = 10x^2 - 6x + 25x - 15 = 10x^2 + 19x - 15. The equation becomes 16x^2 - 3 = 10x^2 + 19x - 15, which simplifies to 6x^2 - 19x + 12 = 0. Since this is in the form ax^2 + bx + c = 0, it is a quadratic equation.

AI explanation

Expand the right side and bring all terms to the left side to check the highest power of x. The right side expands to 10x^2 + 19x - 15, making the equation 16x^2 - 3 = 10x^2 + 19x - 15. Rearranging the terms gives 6x^2 - 19x + 12 = 0. Since the resulting equation is a polynomial with the highest degree of 2, it is a quadratic equation. Therefore, the answer is Yes.

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