Question

find the value of k so that the sum of roots of the quadratic equation 3 X square + 2 k + 1 x minus K + 4 equal to zero is equal to the product of the roots

Answer 1

Let the quadratic equation be
$a {x}^{2} + bx + c = 0$
If
$\alpha \: and \: \beta \: are \: \: root s \: of \: above \: equation$
Products of roots
$\alpha \beta = \frac{c}{a}$
$\alpha + \beta = \frac{ - b}{a}$
Therefore from the question
The equation is
$3 {x}^{2} + (2k + 1)x - (k + 4) = 0$
And also
Product of roots = sum of roots
$\alpha \beta = \alpha + \beta$
$\frac{c}{a} = \frac{ - b}{a}$
Therefore
c=-b
$- (k + 4) = - (2k + 1)$
$k + 4 = 2k + 1$
$4 - 1 = 2k - k$
$3 = k$
Therefore answer is
$k = 3$

Answer 2

here is your answer ...