Question

If x = 2/3 and x = -3 are roots of the quadratic equation 3x^2 + 2kx - 3 =0, find the value of k​

Answer 1

$\red{ \bold{ \large{ \longrightarrow \: \alpha = \frac{2}{3} \: and \: \beta = - 3}}}$

$\red{ \bold{ \large{ \longrightarrow \:sum \: of \: zeroes = \alpha + \beta = \frac{ - b}{a} }}}$

$\red{ \bold{ \large{ \longrightarrow \: \alpha + \beta = \frac{ - b}{a} }}}$

$\red{ \bold{ \large{ \longrightarrow \: \frac{2}{3} +( - 3) = \frac{ - (2k)}{3} }}}$

$\red{ \bold{ \large{ \longrightarrow \: \frac{2 - 9}{3} = \frac{ - (2k)}{3} }}}$

$\red{ \bold{ \large{ \longrightarrow \: \frac{ - 7}{3} = \frac{ - (2k)}{3} }}}$

$\red{ \bold{ \large{ \longrightarrow \: - 7 = - 2k }}}$

$\red{ \bold{ \large{ \longrightarrow \: k = \frac{ - 7}{ - 2} }}}$

$\red{ \bold{ \large{ \longrightarrow \: k = \frac{7}{2} }}}$

$\red{ \bold{ \huge{ \Longrightarrow \: k = 3.5}}}$