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tmua.me Medium Set E Paper 1 · Q7

Paper 1Algebra

For which real values of kk does the equation

x+25−x=k\sqrt{x}+2\sqrt{5-x}=k

have exactly one real solution for xx?

A5≤k≤25\sqrt5\leq k\leq2\sqrt5
B5≤k<25\sqrt5\leq k<2\sqrt5
C5≤k<25 or k=5\sqrt5\leq k<2\sqrt5\ \text{or}\ k=5
D5<k<25 or k=5\sqrt5<k<2\sqrt5\ \text{or}\ k=5
E25<k≤52\sqrt5<k\leq5
Fk=5k=5

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