TS EAMCET · Maths · Quadratic Equation
Let \(S\) be the set of all possible integral values of \(\lambda\) in the interval \((-3,7)\) for which the roots of the quadratic equation \(\lambda x^2+13 x+7=0\) are all rational numbers. Then the sum of the elements in \(S\) is
- A 4
- B 2
- C 3
- D 1
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
We have, \(\begin{aligned} & \lambda x^2+13 x+7 & =0 \\ \therefore & D & =(13)^2-4(\lambda)(7)=169-28 \lambda \end{aligned}\) \(\therefore \quad D=(13)^2-4(\lambda)(7)\) So, \(\lambda \in(-3,7)\) has values \(-2,0,6\) so that \(D\) become perfect square. \(\therefore\) Required…
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