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If a,b are real, then the roots of the quadratic equation (a-b)x 2 - 5(a+b)x -2(a-b)=0 are :- Real and equal. Non-real complex. Real nad unequal. None of these.

If a,b are real, then the roots of the quadratic equation (a-b)x2 - 5(a+b)x -2(a-b)=0 are :-
  1. Real and equal.
  2. Non-real complex.
  3. Real nad unequal.
  4. None of these.

Grade:Select Grade

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

a, b are real.
(a-b)x^2 - 5(a+b)x - 2(a-b) = 0
Lets find out delta.
\Delta = (-5(a+b))^{2}-4(a-b)(-2(a-b))
\Delta = 25(a+b)^{2}+8(a-b)^2
(a+b)2and (a-b)2are always positive and greater than zero.
So their sum is also positive and greater than zero.
So discriminent is positive and greater than zero.
So roots are real and unequal.

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