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Let and ( ) be the roots of the equation x^2-8 x+q=0 . If ^2- ^2=16 , then what is the value of q ?

Options

  1. A-15
  2. B-10
  3. C10
  4. D15

Correct answer

D. 15

Step-by-step solution

Given that and ( ) are roots of the equation array ll & x^2-8 x+q=0 & + =8 and =q & ( - )^2=( + )^2-4 =64-4 q & ( - )= 64-4 q ( ) array aligned & Now ^2- ^2=16 & ( + )-( - )=16 & 8 64-4 q =16 64-4 q =2 & 64-4 q=4 q=15 aligned

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