Question

If the sum of three roots of the equation $x^4+x^3-19x^2-49x-30=0$ is zero, then the fourth root will be

• A. -1

Answer 1

The correct option is A -1
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 $x^4+x^3-19x^2-49x-30=0$ with general form of 4 degree polynomial equation, we get
$a=1,b=1,c=-19,d=-49,e=-30$ and $\alpha +\beta +\gamma =0$
$\Rightarrow \text{Sum of roots}=\alpha +\beta +\gamma +\delta =\frac{-b}{a}\Rightarrow \delta =\frac{-b}{a}\Rightarrow \delta =\frac{-1}{1}=-1$