Which one of the following is not a quadratic equation
a. (x + 2)² = 2(x + 3)
b. x² + 3x = (-1) (1 - 3x)²
c. (x + 2) (x - 1) = x² - 2x - 3
d. x³ - x² + 2x + 1 = (x + 1)³

Solution:

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.

✦ Try This: Which one of the following is not a quadratic equation?

  1. (x + 2)² = 2(x + 3)
  2. x² + 3x = (-1) (1 - 3x)²
  3. (x + 3) (x - 2) = x² - 2x - 3
  4. x³ - x² + 2x + 1 = (x + 1)³

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4

NCERT Exemplar Class 10 Maths Exercise 4.1 Sample Problem 1

Which one of the following is not a quadratic equation, a. (x + 2)² = 2(x + 3), b. x² + 3x = (-1) (1 - 3x)², c. (x + 2) (x - 1) = x² - 2x - 3, d. x³ - x² + 2x + 1 = (x + 1)³

Summary:

(x + 2) (x - 1) = x² - 2x - 3 is not a quadratic equation

☛ Related Questions:

Math worksheets and
visual curriculum