Question

If (1/3) is a root of quadratic equation x² + kx − (5/9) = 0, then find the value of k.​

Answer 1

Answer:

(1/3)square+k(1/3)-5/9=0 = 1/9+k/3-5/9=0 -4/9+k/3=0 -4+3k/9=0 - 4= -3k

= k=4/3

Answer 2

Putting x=(1/3) in the eqⁿ:

$( \frac{1}{3} {)}^{2} + k( \frac{1}{3} ) - \frac{5}{9} = 0 \\ or \: \: \: \: \: \: \: \frac{1}{9} + \frac{k}{3} - \frac{5}{9} = 0 \\ or \: \: \: \: \: \: \: \frac{1 + 3k - 5}{9} = 0$

$or \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3k - 4 = 0 \\ or \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3k = 4 \\ or \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: k = \frac{4}{3}$

Answer k = (4/3)