TS EAMCET · Maths · Quadratic Equation
If \(k \in R\), then roots of \((x-2)(x-3)=k^2\) are always
- A real and distinct
- B real and equal
- C complex number
- D rational numbers
Answer & Solution
Correct Answer
(A) real and distinct
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} (x-2)(x-3) & =k^2, k \in R \\ \Rightarrow x^2-3 x-2 x+6-k^2 & =0 \\ \Rightarrow \quad x^2-5 x+6-k^2 & =0 \end{aligned} \] Now, discriminant \(D=(-5)^2-4(1)\left(6-k^2\right)\)…
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