Which one of the following is not a quadratic equation? Write the equation in standard form and then give the answer.
a. (x+2)2 = 2(x+3)
b. (x+2)(x−1) = x2 − 2x − 5
c. x3 − x2 + 2x + 1 = (x+1)3
Answers
Answer:
See below
Step-by-step explanation:
(a) => (x + 2)² = 2(x + 3)
=> x² + 4x + 4 = 2x + 6
=> x² + 2x - 2 = 0
Hence given equation is quadratic
(b) => (x + 2)(x - 1) = x² - 2x - 5
=> x² + x - 2 = x² - 2x - 5
=> 3x +3 = 0
Hence given equation is not quadratic
(c) => x³ - x² + 2x + 1 = (x + 1)³
=> x³ - x² + 2x + 1 = x³ + 1 + 3x² + 3x
=> 4x² + x = 0
Hence given equation is quadratic
Answer:
a. (x + 2)^2 = 2x + 6
=> x^2 + 4 + 4x = 2x + 6
=> x^2 + 2x - 2 = 0
Hence its a quadratic
c. The degree of the polynomial is 1 after opening brackets, so discard it too.
b. Here the degree also remains 1. Because if you open the brackets, the x^2 term cancels out.
General form of Quadratic equation:
ax^2 + bx + c = 0
Hope this helped.
Edit: For question (a) I thought it was 2(x+2), sorry for that.