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Exponential equations reducible to quadratics; parameter analysis

mathematical

Consider the equation

2^{2x+1} - 5\cdot 2^x + k = 0

Facts you may need

$2^{2x+1} = 2(2^x)^2$ — Index laws.
$y = 2^x > 0$ always — Only positive $y$ values are allowed.
Product of roots $= \frac ca$ ; discriminant $b^2 - 4ac$ — To decide signs and number of roots.

Solve the equation when

k = 2

Find all values of

k

for which the equation has exactly one real solution.