AP EAMCET · Maths · Quadratic Equation
The set of all values of \(k\) for which the inequality \(x^2-(3 \mathrm{k}+1)\) \(x+4 \mathrm{k}^2+3 \mathrm{k}-3\gt0\) is true for all real values of \(x\) is
- A \(\left(-\frac{13}{7}, 1\right)\)
- B \(\left(-1, \frac{13}{7}\right)\)
- C \(\left(-\infty,-\frac{13}{7}\right) \cup(1, \infty)\)
- D \((-\infty,-1) \cup\left(\frac{13}{7}, \infty\right)\)
Answer & Solution
Correct Answer
(C) \(\left(-\infty,-\frac{13}{7}\right) \cup(1, \infty)\)
Step-by-step Solution
Detailed explanation
Since, \(x^2-(3 k+1) x+4 k^2+3 k-3>0 \forall x \in R\) So, \(1\gt0\) and \(b^2-4 a c \lt 0\) \(\begin{aligned} & \Rightarrow\{-(3 k+1)\}^2-4 \times 1 \times\left(4 k^2+3 k-3\right) \lt 0 \\ & \Rightarrow(7 k+13)(k-1)\gt0 \end{aligned}\) So,…
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