AP EAMCET · Maths · Quadratic Equation
Let \(H(x)=3 x^4+6 x^3-2 x^2+1\) and \(g(x)\) be a linear polynomial. If \(\frac{H(x)}{(x-1)(x+1)(x-2)}=f(x)+\frac{g(x)}{(x-1)(x+1)(x-2)}\), then \(H(-1)+2 H(2)-3 H(1)=\)
- A \(f(-1)+2 f(2)-3 f(1)\)
- B \(\mathrm{H}(-1)+\mathrm{f}(2)+\mathrm{g}(3)\)
- C \(g(-1)+2 g(2)-3 g(1)\)
- D \(\mathrm{H}(1)+2 \mathrm{f}(2)-\mathrm{g}(1)\)
Answer & Solution
Correct Answer
(C) \(g(-1)+2 g(2)-3 g(1)\)
Step-by-step Solution
Detailed explanation
\(H(x) = f(x)(x-1)(x+1)(x-2) + g(x)\) At \(x=-1\): \(H(-1) = f(-1)(-1-1)(-1+1)(-1-2) + g(-1) = 0 + g(-1) \implies H(-1)=g(-1)\) At \(x=1\): \(H(1) = f(1)(1-1)(1+1)(1-2) + g(1) = 0 + g(1) \implies H(1)=g(1)\) At \(x=2\):…
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