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
- a is the coefficient of x²
- b is the coefficient of x
- c is the numerical term
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
Learn more:
You can learn more about quadratic equations in brainly.com/question/9390381
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