Q:

write the following quadratic equation to standard form and find a,b,c1) 2x²=3x2)4x²-10=53)3(x²-4x)=2(x+2)4)3x(x+2x)=115)6x(x-8)=2x²+4​

Accepted Solution

A:
1) The standard form of the equation is 2x² - 3x = 0, a = 2 , b = -3 , c = 02) The standard form of the equation is 4x² - 15 = 0, a = 4 , b = 0 , c = -153) The standard form of the equation is 3x² - 14x - 4 = 0, a = 3 , b = -14 , c = -44) The standard form of the equation is 9x² - 11 = 0, a = 9 , b = 0 , c = -115) The standard form of the equation is 4x² - 48x - 4 = 0, a = 4 , b = -48 , c = -4Step-by-step explanation:The standard form of a quadratic equation is ax² + bx + c = 0, wherea is the coefficient of x²b is the coefficient of xc is the numerical term1)∵ 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 = 0The standard form of the equation is 2x² - 3x = 0, a = 2 , b = -3 , c = 02)∵ 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 = -15The standard form of the equation is 4x² - 15 = 0, a = 4 , b = 0 , c = -153)∵ 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 = -4The standard form of the equation is 3x² - 14x - 4 = 0, a = 3 , b = -14 ,c = -44)∵ 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 = -11The standard form of the equation is 9x² - 11 = 0, a = 9 , b = 0 , c = -115)∵ 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 = -4The standard form of the equation is 4x² - 48x - 4 = 0, a = 4 , b = -48 , c = -4Learn more:You can learn more about quadratic equations in brainly.com/question/9390381#Learnwith Brainly