Question

Which of the following is not a quadratic equation?

• A. $-2x+5x^2+2=0$
• B. $3x^2+4x=0$
• C. $\sqrt{x}+\frac{7}{\sqrt{x}}=4\sqrt{x}(x\ne 0)$
• D. $\frac{1}{3x}+3x=4(x\ne 0)$

Answer 1

The correct option is C $\sqrt{x}+\frac{7}{\sqrt{x}}=4\sqrt{x}(x\ne 0)$

Consider the equation $3x^2+4x=0$
It can be rewritten as $3x^2+4x+0=0$, which is in the form of $a{x}^2+bx+c=0$, where $a\ne 0$
$\therefore 3x^2+4x=0$ is a quadratic equation.
Now, consider the equation $-2x+5x^2+2=0$
It can be rewritten as $5x^2-2x+2=0$, which is in the form of $a{x}^2+bx+c=0$, where $a\ne 0$
$\therefore -2x+5x^2+2=0$ is a quadratic equation.
Now, consider the equation,
$\sqrt{x}+\frac{7}{\sqrt{x}}=4\sqrt{x}(x\ne 0)$
$\Rightarrow \frac{x+7}{\sqrt{x}}=4\sqrt{x}$
$\Rightarrow x+7=4x$
$\Rightarrow 3x-7=0$, which is not in the form of $a{x}^2+bx+c=0$, where $a\ne 0$
$\therefore \sqrt{x}+\frac{7}{\sqrt{x}}=4\sqrt{x}(x\ne 0)$ is not a quadratic equation.
Now, consider the equation,
$\frac{1}{3x}+3x=4(x\ne 0)$
$\Rightarrow \frac{1+9x^2}{3x}=4$
$\Rightarrow 1+9x^2=12x$
$\Rightarrow 9x^2-12x+1=0$, which is in the form of $a{x}^2+bx+c=0$, where $a\ne 0$
$\therefore \frac{1}{3x}+3x=4(x\ne 0)$ is a quadratic equation.
Hence, the correct answer is option (3).