NIMCET 2016 Question Paper with solutions

Question : 85 of 120

Marks: +1, -0

Sum of the roots of the equations

4^x

- 3 (

2^{x+3}

) + 128 = 0 is;

Solution:

Given equation is

4^x-3(2^{x+3})+128=0

..(i)
Put

2^x=y

in Eq. (i), we get

⇒(2^{x})^{2}-3(2^{x}⋅2^{3})+128=0

⇒y^{2}-3(8y)+128=0

⇒y^{2}-24y+128=0

⇒y^{2}-16y-8y+128=0

⇒y(y-16)-8(y-16)=0

⇒(y-16)(y-8)=0

⇒y=16,8

⇒2^{x}=16

2^{x}=8

⇒2^{x}=2^{4}

2^{x}=2^{3}

⇒x=4,3

∴ Sum of the root

=4+3=7

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