Please solve and explain in an easy understandable form.
Question) Jim and Tim were studying progressions and their properties. They wrote a quadratic equation, ax2 - 2bx + c = 0 and assumed that a, b and c were in GP. They both had their own theories about the nature of the roots. Tim claimed that the equation had real roots and that the roots were unequal and distinct while Jim claimed that the roots were imaginary.
Which of the following statements is true?
(A) Tim was correct
(B) Jim was correct.
(C) Both Tim and Jim were correct.
(D) Neither Tim nor Jim was correct.
Since a,b and c are in Geometric progression,
Let's assume that a = k / r , b = k and c = k r
Now,
D = (-2 k)2 - 4 (k / r) ( k r) [... D = (-2 b)2 - 4 ac ]
= 4 k2 - 4 k2
= 0
Therefore, we can conclude that roots are real and equal.
hence, Neither Tim nor Jim was correct. (Option D is correct)
Let's assume that a = k / r , b = k and c = k r
Now,
D = (-2 k)2 - 4 (k / r) ( k r) [... D = (-2 b)2 - 4 ac ]
= 4 k2 - 4 k2
= 0
Therefore, we can conclude that roots are real and equal.
hence, Neither Tim nor Jim was correct. (Option D is correct)