1.

Check whether the following are quadratic equationsi) (x–2) (x+1)= (x–1) (x+3)ii) (x–3)(2x+1)=x(x+5)iii)(2x–1)(x–3)=(x+5)(x–1)solve it and answer it ​

Answer»

ANSWER :

  1. No
  2. Yes
  3. Yes

Solution:

1) (x-2)(x+1) = (x-1) (x+3)

⇢x(x+1) -2 (x+1) = x(x+3) -1 (x+3)

⇢x² + x -2X -2 = x² +3x -x -3

⇢x² - x -2 = x² +2x -3

⇢x² - x² - x -2x = -3 +2

⇢-3x = -1

⇢3x = 1

Here , the degree of polynomial is 1 , hence it is a linear equation not a QUADRATIC equation .

2) (x-3) (2x+1) = x(x+5)

⇢x(2x+1) -3 (2x+1) = x² + 5x

⇢2x² + x - 6 x -3 = x² + 5x

⇢2x² - 5x -3 = x² + 5x

⇢2x² - x² -5x -5x - 3 = 0

⇢x² -10x -3 = 0

Here , the degree of polynomial is 2 . Hence it is a quadratic equation.

3) (2x -1) (x-3) = (x+5)(x-1)

⇢2x (x-3) -1(x-3) = x(x-1) +5(x-1)

⇢2x² - 6x - x + 3 = x² - x +5x -5

⇢2x² -7x +3 = x² +4x -5

⇢2x² - x² - 7x -4x +3 +5 = 0

⇢x² - 11 x +10 = 0

Here , the degree of polynomial is 2 . Hence it is a quadratic equation .



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