If the sum of the roots of the equation lambd | vedclass

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

Question

(D) For a quadratic equation $ax^2 + bx + c = 0$,the sum of the roots is given by $-\frac{b}{a}$ and the product of the roots is given by $\frac{c}{a}

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) For a quadratic equation $ax^2 + bx + c = 0$,the sum of the roots is given by $-\frac{b}{a}$ and the product of the roots is given by $\frac{c}{a}$.Given the equation $\lambda x^2 + 2x + 3\lambda = 0$,we have $a = \lambda$,$b = 2$,and $c = 3\lambda$.Sum of the roots $= -\frac{2}{\lambda}$.Product of the roots $= \frac{3\lambda}{\lambda} = 3$.According to the problem,the sum of the roots is equal to their product:$-\frac{2}{\lambda} = 3$.Multiplying both sides by $\lambda$,we get $-2 = 3\lambda$.Therefore,$\lambda = -\frac{2}{3}$.Since $-\frac{2}{3}$ is not among the options $A, B,$ or $C$,the correct option is $D$.

If the sum of the roots of the equation $\lambda x^2 + 2x + 3\lambda = 0$ is equal to their product,then $\lambda = $

Similar Questions

Solve the given two equations and provide the correct answer from the given options.
$I.$ $x^{2}-82x+781=0$
$II.$ $y^{2}-5041=0$

Solve the given two equations and select the correct option.
$I.$ $\frac{x}{x-11} + \frac{x-11}{x} = 7$
$II.$ $\frac{4y}{4y-13} + \frac{4y-13}{4y} = 9$

The value of $k$ for which the equation $2x^2 - kx + x + 8 = 0$ has equal and real roots is:

If $\alpha$ and $\beta$ are the roots of the equation $a x^{2}+b x+c=0$,find the value of $\alpha^{2}+\beta^{2}$.

Solve the given two equations and select the correct option.
$I.$ $2x^2 + 23x + 63 = 0$
$II.$ $4y^2 + 19y + 21 = 0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module