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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

Similar Questions

If one root of the equation $ax^3+bx+c=0$ is twice another root,then

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x+6=0$,then $\Sigma \alpha^2 \beta+\Sigma \alpha \beta^2$ is equal to :

Let $\alpha$ and $\beta$ be the roots of the equation $5x^{2} + 6x - 2 = 0$. If $S_{n} = \alpha^{n} + \beta^{n}$ for $n = 1, 2, 3, \dots$,then:

If $p$ and $q$ are the roots of the equation $x^{2}+px+q=0$, then:

If $\sin \alpha$ and $\cos \alpha$ are the roots of the equation $x^{2}-bx+c=0$, then which of the following statements is/are correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module