If alpha and beta are the roots of the equati | 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 the equation $2x^{2} - 3x + 1 = 0$.From the properties of quadratic equations,the sum of roots $\

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Given that $\alpha$ and $\beta$ are the roots of the equation $2x^{2} - 3x + 1 = 0$.From the properties of quadratic equations,the sum of roots $\alpha + \beta = -(-3)/2 = 3/2$ and the product of roots $\alpha\beta = 1/2$.We need to form a quadratic equation whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$.Let $S$ be the sum of the new roots:$S = \frac{\alpha}{\beta} + \frac{\beta}{\alpha} = \frac{\alpha^{2} + \beta^{2}}{\alpha\beta} = \frac{(\alpha + \beta)^{2} - 2\alpha\beta}{\alpha\beta}$.Substituting the values: $S = \frac{(3/2)^{2} - 2(1/2)}{1/2} = \frac{9/4 - 1}{1/2} = \frac{5/4}{1/2} = 5/2$.Let $P$ be the product of the new roots:$P = \frac{\alpha}{\beta} 	imes \frac{\beta}{\alpha} = 1$.The required quadratic equation is given by $x^{2} - Sx + P = 0$.Substituting $S$ and $P$: $x^{2} - (5/2)x + 1 = 0$.Multiplying by $2$,we get $2x^{2} - 5x + 2 = 0$.

If $\alpha$ and $\beta$ are the roots of the equation $2x^{2} - 3x + 1 = 0$,form an equation whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$.

Similar Questions

If the roots of the equation $\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}$ are equal in magnitude but opposite in sign,then the product of the roots will be

$I. \quad p^{2}-18 p+77=0$
$II. \quad 3 q^{2}-25 q+28=0$
$Quantity \, 1$: Value of $p$
$Quantity \, 2$: Value of $q$

Solve the given two equations and select the correct answer from the given options.
$I.$ $4x + 7y = 209$
$II.$ $12x - 14y = -38$

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-6x=7$
$II.$ $2y^{2}+13y+15=0$

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 6x + a = 0$ and satisfy the relation $3\alpha + 2\beta = 16$,then the value of $a$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module