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Question

The maximum possible number of real roots of equation x56x24x+λ2=0is


Solution

f(x)=x56x24x+λ2=0

+      +

2 changes of sign maximum two positive roots.

f(x)=x56x2+4x+λ2

              +       +

1 change of sign maximum one negative roots.

total maximum possible number of real roots = 2 + 1 = 3.

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