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KVPY2017MathematicsQuadratic Equation

Let a, b, c, d be real numbers between -5 and 5 such that |a|= 4- 5-a ,|b|= 4+ 5-b , |c|= 4- 5+c ,|d|= 4+ 5+d Then the product abcd is

Options

  1. A11
  2. B-11
  3. C121 ,
  4. D-121

Correct answer

A. 11

Step-by-step solution

Given | a |= 4- 5- a squaring array c a²=4- 5-a a⁴+16-8 a²=5-a a⁴-8 a²+a+11=0 array Sirnilarly squaring other given equations & solving we can say that a, b,-c,-d are roots of x⁴-8 x²+x+11=0 product of roots a b(-c)(-d)=11 abcd =11

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