TS EAMCET · Maths · Quadratic Equation
The set of all values of ' \(a\) ' for which the expression \(\frac{a x^2-2 x+3}{2 x-3 x^2+a}\) assumes all real values for real values of \(x\), is
- A \([2,3]\)
- B \(R-(2,3)\)
- C \(\phi\)
- D \([1,5]\)
Answer & Solution
Correct Answer
(C) \(\phi\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Let } y=\frac{a x^2-2 x+3}{2 x-3 x^2+a} \\ & \Rightarrow \quad 2 x y-3 x^2 y+a y=a x^2-2 x+3 \\ & \Rightarrow \quad x^2(a+3 y)-2 x(y+1)+3-a y=0 \\ & \text { as } x \in R, D \geq 0 \\ & \therefore \quad 4(y+1)^2-4(a+3 y)(3-a y) \geq 0 \end{aligned} \]…
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