Question

Which of the following is/are quadratic equation?

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

Answer 1

Answer: (A), (B), (C)

$(x+2)(x-2)=-x^2$

$\left(a\right)(x+1{)}^2=2(x-3)$
$\Rightarrow x^2+2x+1=2x-6$
$\Rightarrow x^2+7=0$
This is a quadratic equation.

$\left(b\right)(x-2)(x+1)=(x-1)(x+3)$
$\Rightarrow x^2-x-2=x^2+2x-3$
$\Rightarrow 3x-1=0$
This is NOT a quadratic equation.

$\left(c\right)x^2-2x=(-2)(3-x)\Rightarrow x^2-2x=-6+2x$
$\Rightarrow x^2-4x+6=0$
This is a quadratic equation.

$\left(d\right)(x+2)(x-2)=-x^2\Rightarrow x^2-4=-x^2$
$\Rightarrow 2x^2-4=0$
This is a quadratic equation.