Question

If $a, -a, b$ are the roots of $x^3 - 5x^2 - x + 5 = 0,$ then $b$ is a root of _________

• A. $x^2-3x-10 = 0$
• B. $x^2+5x-30 = 0$
• C. $x^2+3x-20 = 0$
• D. $x^2-5x+10 = 0$

Answer 1

Answer: (A)

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
$f(x) \equiv x^{2}-3 x-10=0$
ie, $f(5) \equiv(5)^{2}-3(5)-10$
$=25-15-10$
$=0$
So, (b) is the roots equation $x^{2}-3 x-10=0$.