Question

The roots of equation $2x^4-9x^3+14x^2-9x+2=0$ are

• A. $(1,2,3,4)$
• B. $(1,1,\frac{1}{2},2)$
• C. $(1,\frac{1}{3},3,1)$
• D. $(0,1,1,\frac{1}{2})$

Answer 1

The correct option is B $(1,1,\frac{1}{2},2)$

We can see that in the giving equation, the multiplication of roots is $1$

i.e multiplication of roots $=\frac{e}{a}$ in the equation $a{x}^4+b{x}^3+c{x}^2+dx+e=0$

$\Rightarrow$ $\frac{e}{a}=\frac{2}{2}=1$

Now, sum of the roots is $\frac{-b}{a}=-\left(\frac{-9}{2}\right)=\frac{9}{2}$

$\Rightarrow$ it is only possible in option B.

Hence, option B is correct.