If alpha and beta are the roots of the quadra | vedclass

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

Question

(C) Given that $\alpha$ and $\beta$ are the roots of $x^2 + bx - c = 0$.By the relation between roots and coefficients:$\alpha + \beta = -b$ and $\alp

Vedclass · Accepted Answer

$x^2 + [(\alpha + \beta) + \alpha \beta]x + \alpha \beta(\alpha + \beta) = 0$

Vedclass · Answer

(C) Given that $\alpha$ and $\beta$ are the roots of $x^2 + bx - c = 0$.By the relation between roots and coefficients:$\alpha + \beta = -b$ and $\alpha \beta = -c$.This implies $b = -(\alpha + \beta)$ and $c = -\alpha \beta$.We need to find the equation whose roots are $b$ and $c$.Sum of the roots = $b + c = -(\alpha + \beta) - \alpha \beta = -[(\alpha + \beta) + \alpha \beta]$.Product of the roots = $bc = [ -(\alpha + \beta) ] 	imes [ -\alpha \beta ] = \alpha \beta(\alpha + \beta)$.The required quadratic equation is $x^2 - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Substituting the values:$x^2 - (-[(\alpha + \beta) + \alpha \beta])x + \alpha \beta(\alpha + \beta) = 0$.$x^2 + [(\alpha + \beta) + \alpha \beta]x + \alpha \beta(\alpha + \beta) = 0$.

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 + bx - c = 0$,then the equation whose roots are $b$ and $c$ is:

Similar Questions

If the difference between the roots of the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ is the same,and $a \neq b$,then:

If $8$ and $2$ are the roots of ${x^2} + ax + \beta = 0$ and $3$ and $3$ are the roots of ${x^2} + \alpha x + b = 0$,then the roots of ${x^2} + ax + b = 0$ are

If the sum of any two roots of the equation $x^3+p x^2+q x+r=0$ is zero,then

If the ratio of the roots of the equation $12x^2 - mx + 5 = 0$ is $2 : 3$,then $m = .....$

The value of $p$ for which the sum of the squares of the roots of the equation $x^2 - (p + 3)x + (5p - 2) = 0$ assumes its least value is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module