Find the value of k so that the sum of the ro | vedclass

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(A) The given quadratic equation is $3 x^{2}+(2 k+1) x-(k+5)=0$.Comparing this with the standard form $a x^{2}+b x+c=0$,we identify the coefficients a

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$4$

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(A) The given quadratic equation is $3 x^{2}+(2 k+1) x-(k+5)=0$.Comparing this with the standard form $a x^{2}+b x+c=0$,we identify the coefficients as $a=3$,$b=2 k+1$,and $c=-(k+5)$.The sum of the roots is given by $\frac{-b}{a} = \frac{-(2 k+1)}{3}$.The product of the roots is given by $\frac{c}{a} = \frac{-(k+5)}{3}$.According to the problem,the sum of the roots is equal to the product of the roots:$\frac{-(2 k+1)}{3} = \frac{-(k+5)}{3}$.Multiplying both sides by $3$,we get $-(2 k+1) = -(k+5)$.This simplifies to $2 k+1 = k+5$.Subtracting $k$ from both sides,we get $k+1 = 5$.Therefore,$k = 4$.

Find the value of $k$ so that the sum of the roots of the equation $3 x^{2}+(2 k+1) x-k-5=0$ is equal to the product of the roots:

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