Explanation:
quadratic equations are second-degree polynomials (algebraic expressions) and are of the form
ax² + bx + c = 0
"a" must not be 0, of course. otherwise it would be a linear equation (bx + c = 0).
so,
1. is NOT quadratic, because a = 0 (there is no x² term).
2. is quadratic, because the whole equating can be transformed into
7x² + ½x - 2 = 0
and after multiplying by 2 it is even
14x² + x - 4 = 0
3. is NOT quadratic, because the x² term is removed when transforming the whole equation to standard form :
7 + x² = 7x + x² - 5 | subtract x² on both sides
7 = 7x - 5 | subtract 7 from both sides
0 = 7x - 12
4. is NOT quadratic, because the highest exponent of the variable is 3 (instead of 2).
5. is a quadratic expression but NOT a quadratic equation, because there is no equation (nothing where something is set to be equal to something else).
6. is quadratic after simplifying and transforming :
x(x + 5)² - x³ = 1
x(x² + 10x + 25) - x³ = 1
x³ + 10x² + 25x - x³ = 1
10x² + 25x = 1
10x² + 25x - 1 = 0
7. is a quadratic expression but NOT a quadratic equation, because there is no equation (see 5.).
8. is quadratic, as we can transform this into the standard form :
x² = -x - 22
x² + x = -22
x² + x + 22 = 0
9. is quadratic, as after simplifying we get the standard form :
(x + 1)(x + 1) = 9
x² + 2x + 1 = 9
x² + 2x - 8 = 0
10. is quadratic, as we can transform this into the standard form
23 = 7x² - x
0 = 7x² - x - 23