Write the following quadratic equation to standard form and find a, b,c

1) 2x²=3x
2)4x²-10=5
3)3(x²-4x)=2(x+2)
4)3x(x+2x)=11
5)6x(x-8)=2x²+4

1) The standard form of the equation is 2x² - 3x = 0, a = 2 , b = -3 ,

c = 0

2) The standard form of the equation is 4x² - 15 = 0, a = 4 , b = 0 ,

c = -15

3) The standard form of the equation is 3x² - 14x - 4 = 0, a = 3 , b = -14 ,

c = -4

4) The standard form of the equation is 9x² - 11 = 0, a = 9 , b = 0 ,

c = -11

5) The standard form of the equation is 4x² - 48x - 4 = 0, a = 4 , b = -48 ,

c = -4

Step-by-step explanation:

The standard form of a quadratic equation is ax² + bx + c = 0, where

1)

∵ 2x² = 3x

- Subtract 3x from both sides

∴ 2x² - 3x = 0

∵ The coefficient of x² = 2

∴ a = 2

∵ The coefficient of x = -3

∴ b = -3

∵ There is no numerical term

∴ c = 0

The standard form of the equation is 2x² - 3x = 0, a = 2 , b = -3 , c = 0

2)

∵ 4x² - 10 = 5

- Subtract 5 from both sides

∴ 4x² - 10 - 5 = 0

- Add like terms

∴ 4x² - 15 = 0

∵ The coefficient of x² = 4

∴ a = 4

∵ There is no x term

∴ b = 0

∵ The numerical term = -15

∴ c = -15

The standard form of the equation is 4x² - 15 = 0, a = 4 , b = 0 , c = -15

3)

∵ 3(x² - 4x) = 2(x + 2)

- Simplify each side

∴ 3x² - 12x = 2x + 4

- Subtract 2x from both sides

∴ 3x² - 12x - 2x = 4

- Subtract 4 from both sides

∴ 3x² - 12x - 2x - 4 = 0

- Add like terms

∴ 3x² - 14x - 4 = 0

∵ The coefficient of x² = 3

∴ a = 3

∵ The coefficient of x = -14

∴ b = -14

∵ The numerical term = -4

∴ c = -4

The standard form of the equation is 3x² - 14x - 4 = 0, a = 3 , b = -14 ,

c = -4

4)

∵ 3x(x + 2x) = 11

- Add the terms in the bracket

∴ 3x(3x) = 11

- Simplify the left hand side

∴ 9x² = 11

- Subtract 11 from both sides

∴ 9x² - 11 = 0

∵ The coefficient of x² = 9

∴ a = 9

∵ There is no x term

∴ b = 0

∵ The numerical term = -11

∴ c = -11

The standard form of the equation is 9x² - 11 = 0, a = 9 , b = 0 ,

c = -11

5)

∵ 6x(x - 8) = 2x² + 4

- Simplify the left hand side

∴ 6x² - 48x = 2x² + 4

- Subtract 2x² from both sides

∴ 4x² - 48x = 4

- Subtract 4 from both sides

∴ 4x² - 48x - 4 = 0

∵ The coefficient of x² = 4

∴ a = 4

∵ The coefficient of x = -48

∴ b = -48

∵ The numerical term = -4

∴ c = -4

The standard form of the equation is 4x² - 48x - 4 = 0, a = 4 , b = -48 ,

c = -4

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step-by-step explanation: