Question

If the sum of three roots of the equation $4x^4+5x^3-33x^2+89x-71=0$ is zero, then the fourth root will be

• A. -1.25

Answer 1

The correct option is A -1.25
Let $\alpha ,\beta ,\gamma ,\delta$ be the roots of the equation $a{x}^4+b{x}^3+c{x}^2+dx+e=0,a\ne 0$
We know sum of roots is given by
$\alpha +\beta +\gamma +\delta =\frac{-b}{a}$

Comparing the given equation $4x^4+5x^3-33x^2+89x-71=0$ with general form of 4 degree polynomial equation, we get
$a=4,b=5,c=33,d=89,e=-71$ and $\alpha +\beta +\gamma =0$
and
$\text{Sum of roots}=\alpha +\beta +\gamma +\delta =\frac{-b}{a}\Rightarrow \delta =\frac{-b}{a}\Rightarrow \delta =\frac{-5}{4}=-1.25$