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Quadratic equation
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Quadratic equation Help me pls​-example-1

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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

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