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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
MathematicsQuadratic EquationKCETKCET 2010
Options:
  • A $x^{2}+3 x-20=0$
  • B $x^{2}-5 x+10=0$
  • C $x^{2}-3 x-10=0$
  • D $x^{2}+5 x-30=0$
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 $x^{2}-3 x-10=0$.

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