Which of the following options does not represent a quadratic equation?
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(4x – 5)2 + 3x = (6x – 2)2 + 8
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19x3 + 14x2 + 8x + 3 = 18x2 + 19x3 + 2
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(7x – 2)2 + 3x + 5 = 8x2 – 3x + 2
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None of these
A quadratic equation must have the highest power of x as 2. Option A: 16x^2 - 40x + 25 + 3x = 36x^2 - 24x + 4 + 8, which simplifies to a quadratic. Option B: 19x^3 terms cancel out, leaving -4x^2 + 8x + 1 = 0, which is quadratic. Option C: 49x^2 - 28x + 4 + 3x + 5 = 8x^2 - 3x + 2, which is quadratic. Since all are quadratic, 'None of these' is correct.
We must check if the given equations simplify to a degree other than two. The first equation expands to 16x2 - 37x + 22 = 36x2 - 20x + 4, which simplifies to 20x2 - 17x - 18 = 0. The second equation cancels the 19x3 terms to become 14x2 + 8x + 1 = 0. The third equation expands to 49x2 - 25x + 9 = 8x2 - 3x + 2, which simplifies to 41x2 - 22x + 7 = 0. Because all three given options simplify to valid quadratic equations, none of them fail to represent one.