Question

If the quadratic equation 3xsquare + 2x + k = 0 has two equal roots, then the value of k

Answer 1

Step-by-step explanation:

b^2-4ac=0

4-12k=0

k=1/3

Answer 2

Step-by-step explanation:

Given,

$\: \: \: \: \: \: 3 {x}^{2} + 2x + k = 0 \: \: \: \: \: has \: two \: equal \: roots \\ therefore \: \: \alpha = \beta$

Here a = 3 , b = 2, c = k

$sum \: of \: roots$

$\: \: \: \: \: \: \alpha + \alpha = \frac{2}{3} \\ = > 2 \alpha = \frac{2}{3} \\ = > \alpha = \frac{1}{3}$

$prouct \: of \: roots$

$\: \: \: \: \: \: \: \: \: \: \alpha \times \alpha = \frac{ - k}{3} \\ = > \alpha {}^{2} = \frac{ - k}{3} \\ = > (\frac{1}{3}){}^{2} = \frac{ - k}{3} \\ = > \frac{1}{9} = \frac{ - k}{3} \\ = > - 9k = 3 \\ = > - k = \frac{3}{9} \\ = > - k = \frac{1}{3} \\ therefore \: \: \: \: \: k = \frac{ - 1}{3}$