TS EAMCET · Maths · Quadratic Equation
If \(f(x)=x^2+b x+c\) and \(f(1+k)=f(1-k) \forall \mathrm{K} \in \mathbb{R}\), for two real numbers b and c, then
- A \(f(1) < f(0) < f(-1)\)
- B \(f(-1) < f(0) < f(1)\)
- C \(f(0) < f(-1) < f(1)\)
- D \(f(0) < f(1) < f(-1)\)
Answer & Solution
Correct Answer
(A) \(f(1) < f(0) < f(-1)\)
Step-by-step Solution
Detailed explanation
Axis of symmetry: \(x=1\) For \(f(x)=x^2+bx+c\), axis of symmetry is \(x=-b/2\). \(-b/2 = 1 \implies b = -2\) \(f(x)=x^2-2x+c\) \(f(0) = 0^2-2(0)+c = c\) \(f(1) = 1^2-2(1)+c = 1-2+c = c-1\) \(f(-1) = (-1)^2-2(-1)+c = 1+2+c = c+3\) Comparing the values: \(c-1…
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