Search any question & find its solution
Question:
Answered & Verified by Expert
If $a,-a, b$ are the roots of $x^{3}-5 x^{2}-x+5=0$, then $b$ is a root of
Options:
Solution:
2317 Upvotes
Verified Answer
The correct answer is:
$x^{2}-3 x-10=0$
Given, $x^{3}-5 x^{2}-x+5=0$
Hare, roots (a, - a, b).
Sum of the roots $=a-a+b=5$
$$
b=5
$$
and $b=5$ satisfies the equation
ie,
$$
\begin{aligned}
f(x) & \equiv x^{2}-3 x-10=0 \\
f(5) & \equiv(5)^{2}-3(5)-10 \\
&=25-15-10 \\
&=0
\end{aligned}
$$
So, (b) is the roots equation $x^{2}-3 x-10=0$.
Hare, roots (a, - a, b).
Sum of the roots $=a-a+b=5$
$$
b=5
$$
and $b=5$ satisfies the equation
ie,
$$
\begin{aligned}
f(x) & \equiv x^{2}-3 x-10=0 \\
f(5) & \equiv(5)^{2}-3(5)-10 \\
&=25-15-10 \\
&=0
\end{aligned}
$$
So, (b) is the roots equation $x^{2}-3 x-10=0$.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.