Question

Which of the following is not a quadratic equation?

• A. $(x–2{)}^2$+ 1 = 2x -3
• B. $(x+2{)}^3$=$x^3$-4
• C. $x(x+1)+8=(x+2)(x–2)$
• D. $x(2x+3)=(x^2+1)$

Answer 1

The correct option is C

$x(x+1)+8=(x+2)(x–2)$

(a) ${(x-2)}^2$+ 1 = (2x – 3)

$x^2$ – 4x + 4 + 1 = 2x - 3

$x^2$ – 4x + 4 + 1 - 2x + 3 = 0

$x^2$ – 6x + 8 = 0

This is a quadratic equation.

(b) $(x+2{)}^3$= $x^3$ – 4

$x^3$ + 6$x^2$ + 12x + 8 = $x^3$ – 4

6$x^2$ + 12x + 12 = 0

This is a quadratic equation.

(c) x(x + 1) + 8 = (x + 2) (x – 2)

$x^2$ + x + 8 = $x^2$ – 4

x+12 = 0

This is not a Quadratic equation.

(d) x(2x + 3) = $x^2$ + 1

2$x^2$ + 3x = $x^2$+1

$x^2$ +3x -1 = 0

This is a quadratic equation.