If x2 + kx + \(\frac{16}{9}\) is a perfect square, find the value of k
-
\(\frac{8}{3}\)
- \(\frac{7}{3}\)
- \(\frac{5}{3}\)
- \(\frac{2}{3}\)
The correct answer is: A
Explanation
x2 + kx + \(\frac{16}{9}\); Perfect square
But, b2 - 4ac = 0, for a perfect square
where a - 1; b = k; c = \(\frac{16}{9}\)
k2 - 4(1) x \(\frac{16}{9}\) = 0
k2 - \(\frac{64}{9}\) = 0
k2 = \(\frac{64}{9}\)
k = \(\sqrt{\frac{64}{9}}\)
k = \(\frac{8}{3}\)