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

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(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

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(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 = $

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