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Which of the following is not a quadratic equation?

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x - \frac{3}{2 x} = 5

4 x - \frac{5}{8} = x^{2}

x + \frac{1}{x} = 9

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

answer is D.

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Detailed Solution

It is given that we have to find the equation which is not quadratic from the given options.
Let’s, simplify all the equations given in options and convert them to standard forms,
Checking for option(1)

x - \frac{3}{2 x} = 5

Now,

x - \frac{3}{2 x} = 5

\Rightarrow \frac{2 x^{2} - 3}{2 x} = 5

\Rightarrow 2 x^{2} - 3 = 10 x

\Rightarrow 2 x^{2} - 10 x - 3 = 0

The highest power of variable

x

2

.
So, it is a quadratic equation.
Checking for option(2)

4 x - \frac{5}{8} = x^{2}

Now,

4 x - \frac{5}{8} = x^{2}

\Rightarrow \frac{32 x - 5}{8} = x^{2}

\Rightarrow 32 x - 5 = 8 x^{2}

\Rightarrow 8 x^{2} - 32 x + 5 = 0

The highest power of variable

x

2

.
So, it is a quadratic equation.
Checking for option(3)

x + \frac{1}{x} = 9

Now,

x + \frac{1}{x} = 9

\Rightarrow \frac{x^{2} + 1}{x} = 9

\Rightarrow x^{2} + 1 = 9 x

\Rightarrow x^{2} - 9 x + 1 = 0

The highest power of variable

x

2

.
So, it is a quadratic equation.
Checking for option(4)

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

Now,

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

\Rightarrow \frac{12 x^{2} - 2}{3 x} = 4 x^{2}

\Rightarrow 12 x^{2} - 2 = 12 x^{3}

\Rightarrow 12 x^{3} - 12 x^{2} + 2 = 0

\Rightarrow 6 x^{3} - 6 x^{2} + 1 = 0

Here, the highest power of variable

x

3

.
So, it is not a quadratic equation.
Hence, 4 is the correct option.

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