WBJEE · Maths · Quadratic Equation
If the equation \(x^{2}+y^{2}-10 x+21=0\) has real roots \(x=\alpha\) and \(y=\beta,\) then
- A \(3 \leq x \leq 7\)
- B \(3 \leq y \leq 7\)
- C \(-2 \leq y \leq 2\)
- D \(-2 \leq x \leq 2\)
Answer & Solution
Correct Answer
(C) \(-2 \leq y \leq 2\)
Step-by-step Solution
Detailed explanation
Given, \(\quad x^{2}+y^{2}-10 x+21=0\) \(\Rightarrow\) \(x^{2}-10 x+y^{2}+21=0\) Now, for real roots of \(x, D \geq 0\) \(\Rightarrow\) \[ \begin{array}{r} 100-4\left(y^{2}+21\right) \geq 0 \\ y^{2} \leq 4 \Rightarrow-2 \leq y \leq 2 \end{array} \] Also.…
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