Respuesta :
Answer:
Quadratic Equations ⇒ D, E, F
Step-by-step explanation:
Let us say that each of these equations can only be defined as a quadratic equation if it can be factored / solved through completing the square / application of quadratic formula as solve for the value of x;
[tex]A. 2x - 1 = 0, Add + 1 to either side,\\2x = 1, Divide sides by 2,\\x = 1 / 2 ; Not Quadratic Equation[/tex]
[tex]B. 2x^2 - 1 = 0, Add + 1 to either side,\\2x^2 = 1, Divide sides by 2,\\x^2 = 2, Take | | of x, \sqrt{x} - either side \\\| x | = \sqrt{1 / 2},\\x = \sqrt{1 / 2} = - \sqrt{1 / 2} ; NotQuadraticEquation[/tex]
[tex]C. 2x^2 - 1, NotInForm - ax^2 + bx + x = 0 ; NotQuadraticEquation[/tex]
[tex]D. 3x^2 + 5x - 1 = 0, Add 1 to either side,\\3x^2 + 5x = 1, Divide sides by 3,\\x^2 + 5x / 3 = 1 / 3, Solve for a,\\2ax = 5 / 3x, Divide sides by 2x,\\a = 5 / 6, Add a^2 - ( 5 / 6 )^2 to either side,\\x^2 + ( 5x / 3 )^2 + ( 5 / 6 )^2 = 1 / 3 + ( 5 / 6 )^2, simplify,\\( x + 5 / 6 )^2 = 37 / 36, solve for x,\\x = ( \sqrt{37} - 5 ) / 6 = ( - \sqrt{37} - 5 ) / 6 ; QuadraticEquation[/tex]
[tex]E. x - x^2 + 5 = 0, Similar Form ; QuadraticEquation\\[/tex]
[tex]F. - 4x^2 + x = 0, Factor the Expression,\\- x * ( 4x - 1 ) = 0, Apply Zero Product Property,\\x = 0, and, 4x - 1 = 0,\\x = 0 = 1 / 4 ; QuadraticEquation[/tex]
