NIMCET 2018 Question Paper with solutions

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Question : 28 of 120

Marks: +1, -0

If o, b, c are the roots of the equation

x^3-3x^2

+ 3x + 7 = 0 , then the value of

|\table 2bc-a^,c^2,b^2;c^2,2ac-b^2,a^2;b^2,a^2,2ac-c^2|

is

9
27
81
0

Solution:

Given equation,

x^3-3x^2+3x+7

= 0
a + b + c = 3
ab + bc + ca = 3
abc = 7 ... (i)
Now ,

|\table 2bc-a^2,c^2,b^2;c^2,2ac-b^2,a^2;b^2,a^2,2ab-c^2|

=

|\table a,b,c;b,c,a;c,a,b|

×

|\table -a,c,b;-b,a,c;-c,b,a|

=

|\table a,b,c;b,c,a;c,a,b|

×

|\table a,b,c;b,c,a;c,a,b|

=

|\table a,b,c;b,c,a;c,a,b|^2

= [a (bc -

a^2

) + b (ac -

b^2

) + c (ab -

c^2

)]
=

[3abc-a^3-b^3-c^3]^2

= 0

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