If a, -a, b are the roots of x^{3}-5x^{2}-x+5 | vedclass

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Question

(C) Given the cubic equation $x^{3}-5x^{2}-x+5=0$. Let the roots be $a, -a, b$. From the relationship between roots and coefficients,the sum of the ro

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Given the cubic equation $x^{3}-5x^{2}-x+5=0$. Let the roots be $a, -a, b$. From the relationship between roots and coefficients,the sum of the roots is given by: $a + (-a) + b = -(-5)/1 = 5$. This simplifies to $b = 5$. Now,we check which of the given quadratic equations is satisfied by $x = 5$: For option $C$,$x^{2}-3x-10=0$: Substituting $x = 5$,we get $(5)^{2}-3(5)-10 = 25-15-10 = 0$. Since the equation is satisfied,$b=5$ is a root of $x^{2}-3x-10=0$.

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

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