Question

Which of the following is a quadratic equation ?

• A. $6x^2=20-x^3$
• B. $x^2-\left(\frac{1}{x^2}\right)$ = $\frac{7}{2}$
• C. $\frac{3}{x}$ $=4$ $x^2$
• D. $5x^2+7=3x$

Answer 1

The correct option is D $5x^2+7=3x$

For $\left(A\right)$

$6x^2=20-x^3$

$\Rightarrow x^3+6x^2-20=0$

In this, the maximum power of $x$ is $3$.

So, it is not a quadratic equation.

For $\left(B\right)$

$x^2-\left(\frac{1}{x^2}\right)=\frac{7}{2}$

$\Rightarrow 2x^4-2=7x^2$

$\Rightarrow 2x^4-7x^2-2=0$

In this, the maximum power of $x$ is $4$.

So, it is not a quadratic equation.

For $\left(C\right)$

$\frac{3}{x}=4x^2$

$\Rightarrow 3=4x^3$

In this, the maximum power of $x$ is $3$.

So, it is not a quadratic equation.

For $\left(D\right)$

$5x^2+7=3x$

$\Rightarrow 5x^2-3x+7=0$

In this, the maximum power of $x$ is $2$.

So, it is a quadratic equation.

Hence, $Op-D$ is correct.