If a, -a, b are the roots of x3 - 5x2 - x + 5 = 0, then b is a root of

Question

If a, -a, b are the roots of x3 - 5x2 - x + 5 = 0, then b is a root of  (A) x2-3x-10 = 0 (B) x2+5x-30 = 0 (C) x2+3x-20 = 0 (D) x2-5x+10 = 0

Tardigrade Admin · Accepted Answer

Given, x3-5 x2-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) ≡ x2-3 x-10=0 ie, f(5) ≡(5)2-3(5)-10 =25-15-10 =0 So, (b) is the roots equation x2-3 x-10=0.

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

$x^{2} - 3 x - 10 = 0$

$x^{2} + 5 x - 30 = 0$

$x^{2} + 3 x - 20 = 0$

$x^{2} - 5 x + 10 = 0$

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

Q. If a,−a,b are the roots of x3−5x2−x+5=0, then b is a root of _________

x2−3x−10=0

x2+5x−30=0

x2+3x−20=0

x2−5x+10=0