GATE EC 2020 Set 1 — Question 9
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
are real numbers. The quadratic equation has equal roots, which is eta, then
Correct answer
(C) β³ = bc/(2a²)
Solution
For a quadratic equation of the form , the roots are equal if the discriminant . In the given equation :
1.The discriminant is .
2.For equal roots, .
3.The value of the equal roots is given by the formula .
Now, let's evaluate the options:- (A) : Incorrect, as .
- (B) : . Substituting , we get . Thus, is incorrect.
- (C) :
- LHS: .
- RHS: .
- Since LHS = RHS, this option is correct.
- (D) : Incorrect, as is the condition for equal roots.
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