NIMCET 2009 Question Paper with solutions

Question : 34 of 120

Marks: +1, -0

The number of distinct integral values of 'a' satisfying the equation

2^{2 a}-3(2^{a+2})+2^{5}=0

Solution:

2^{2 a}-3(2^{a+2})+2^{5}=0

Let

y=2^{a}

⇒ y^{2}-12 y+32=0

⇒(y-4)(y-8)=0

⇒ \;\; y=4,8

2^{a}=4 ⇒ a=2

2^{a}=8 ⇒ a=3

Thus, the number of integrals satisfying a is 2 (two).

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