which of the following is not a quadratic equation 1)(2X+1)(x+1) =x² -2( x+ 1)(x+2)(x+3) =( x+4)x²=4x(x+1)=0
Answers
Step-by-step explanation:
We have to find the quadratic equation.
The standard form of a quadratic equation is ax2 + bx + c = 0 in variable x.
Where a, b, and c are real numbers and a ≠ 0.
We need to check if the degree of the given equations is 2.
From the options,
A) (x + 2)² = 2(x + 3)
By using algebraic identity,
(a + b)² = a² + 2ab + b²
x² + 4x + 4 = 2x + 6
x² + 4x - 2x + 4 - 6 = 0
x² + 2x - 2 = 0
The degree of the equation is 2.
Therefore, (x + 2)² = 2(x + 3) is a quadratic equation.
B) x² + 3x = (-1) (1 - 3x)²
By using algebraic identity,
(a - b)² = a² - 2ab + b²
x² + 3x = -1(1 - 6x + 9x²)
x² + 3x = -1 + 6x - 9x²
x² + 9x² + 3x - 6x + 1 = 0
10x² - 3x + 1 = 0
The degree of the equation is 2.
Therefore, x² + 3x = (-1)(1 - 3x) is a quadratic equation.
C) (x + 2) (x - 1) = x² - 2x - 3
By multiplicative and distributive property,
x² - x + 2x - 2 = x² - 2x - 3
By grouping,
x² - x² - x + 2x + 2x - 2 + 3 = 0
3x + 1 = 0
The degree of the equation is 1.
Therefore, (x + 2) (x - 1) = x² - 2x - 3 is not a quadratic equation.
D) x³ - x² + 2x + 1 = (x + 1)³
By using algebraic identity,
(a + b)³ = a³ + b³ + 3a²b + 3ab²
x³ - x² + 2x + 1 = x³ + 1 + 3x² + 3x
x³ - x³ - x² - 3x² + 2x - 3x + 1 = 0
-4x² - x + 1 = 0
4x² + x - 1 = 0
The degree of the equation is 2.
Therefore, x³ - x² + 2x + 1 = (x + 1)³ is a quadratic equation.