Which among the following equations has roots which are negatives of the roots of the equation…
Which among the following equations has roots which are negatives of the roots of the equation \(x^3-x^2+x-4=0\) ?
\(x^3-x^2+x-4=0\)
\(x^3+x^2+x+4=0\)
\(x^3-x^2+x-4=0\)
\(x^3-x^2-x-4=0\)
Solution
Let \(\alpha\) is the root of equation
\(x^3-x^2+x-4=0\)
Now, put \((-\alpha)=x\), so we get the required equation, and it is
\(\begin{aligned}
& (-x)^3-(-x)^2+(-x)-4=0 \\
& \Rightarrow \quad-x^3-x^2-x-4=0 \\
& \Rightarrow \quad x^3+x^2+x+4=0 \\
\end{aligned}\)