AP EAMCET · Maths · Quadratic Equation
If \(x\) is real, then the sum of the maximum and the minimum values of the expression \(\frac{x^2+4 x+1}{x^2+x+1}\) is
- A -2
- B 2
- C 1
- D 0
Answer & Solution
Correct Answer
(D) 0
Step-by-step Solution
Detailed explanation
\((y-1)x^2 + (y-4)x + (y-1) = 0\) \(D \ge 0 \implies (y-4)^2 - 4(y-1)(y-1) \ge 0\) \(y^2 - 8y + 16 - 4(y^2 - 2y + 1) \ge 0\) \(-3y^2 + 12 \ge 0 \implies 3y^2 - 12 \le 0\) \(y^2 - 4 \le 0 \implies (y-2)(y+2) \le 0\) \(-2 \le y \le 2\) Max value \( = 2 \), Min value \( = -2 \) Sum…
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