If x2 kx frac 16 9 is a perfect square find the... - WAEC Mathematics 2010 Question
If x2 + kx + \(\frac{16}{9}\) is a perfect square, find the value of k
A
\(\frac{8}{3}\)
B
\(\frac{7}{3}\)
C
\(\frac{5}{3}\)
D
\(\frac{2}{3}\)
correct option: a
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 = \(\frac{8}{3}\)
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