Question

The equation $2x^4-9x^3+14x^2-9x+2=0$ is of the type

• A. Quadratic equation
• B. Linear equation
• C. Reciprocal Equation
• D. None

Answer 1

Answer: (C)

Reciprocal Equation

Given equation is $2x^4-9x^3+14x^2-9x+2=0$ .... $\left(i\right)$

The maximum power of $x$ in this equation is $4$, so this is $4th$ degree equation

So, it is neither linear nor quadratic equation.

In reciprocal equation $a{x}^4+b{x}^3+c{x}^2+dx+e=0$, the multiplication of the roots i.e ($\frac{e}{a}$) should be $1$

In the given equation $\left(i\right)$, $\frac{e}{a}=\frac{2}{2}$

So the multiplication of roots is equal to one

Therefore, equation $\left(i\right)$ is a reciprocal equation.

Hence, option C is correct.