Question
Determine the exact value of k so that the quadratic function f(x) = x2 - kx + 5 has only one zero.
Answers
Reiny
to have one root, (actually two equal roots)
b^2 - 4ac = 0
k^2 - 4(1)(5) = 0
k^2 = 20
k = ± √20 = ± 2√5
check:
x^2 + 2√5x + 5 = (x + √5)^2
x^2 - 2√5x + 5) = (x - √5)^2
b^2 - 4ac = 0
k^2 - 4(1)(5) = 0
k^2 = 20
k = ± √20 = ± 2√5
check:
x^2 + 2√5x + 5 = (x + √5)^2
x^2 - 2√5x + 5) = (x - √5)^2