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Which of the following can be expressed in the form of a standard quadratic equation?
Question

Which of the following can be expressed in the form of a standard quadratic equation?

A.

(2x1)3=x23x+2(2x-1)^3=x^2-3x+2​​

B.

(2x2+3x4)2x+5=0√(2x^2+3x-4)-2x+5=0​​

C.

(x+1)(x+2)=x216(x+1)(x+2)=x^2-16​​

D.

(2x+3)2+4x5=(2x+1)(2x3)(2x+3)^2+4x-5=(2x+1)(2x-3)​​

Correct option is B

Solution: 
From the options;
Option (a): 
( 2x - 1)3 = x2 - 3x + 2 
(2x)3 + (1)3 + 2 (2x)2 (-1) + 2 (2x) (-1)2
8x3 + 1 - 8x2 + 4x - x2 3x -2 = 0
8x3 + 9x2 7x - 1 = 0 
This  is not quadratic equation  
Option (b):  
(2x2+3x4)2x+5=0\sqrt{(2x^2 + 3x -4)} -2x + 5 = 0
2x2+3x42x+5=0\sqrt{ 2x^2 + 3x - 4 - 2x + 5} = 0
=2x2+x+1\sqrt{ 2x^2 + x + 1}
x2 +2x\sqrt2x + 1 = 0 
This is quadratic  equation 
Option(c): 
(x + 1) (x + 2) = x2 - 16
x (x + 2) +1(x + 2) = x2 - 16
\3x + 2 + 18 = 0
3x + 20 = 0 
This is not quadratic equation
Option(d);   
(2x + 3)2 + 4x - 5 = (2x + 1) (2x - 3)
(2x)2 + (3)2 + (2) (2x) (3) + 4x -5  = (2x + 1)(2x - 3)
4x2 + 9 12x + 4x - 5 = 4x 2​- 6x + 2x - 3 
4 + 16x + 6x - 2x + 3 = 0 
7 + 22x - 2x = 0 
7 + 20x = 0 
This is not quadratic equation
Thus, the correct option is : (b)

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