AP EAMCET · Maths · Quadratic Equation
If \(f(x)=x^4-2 x^3+3 x^2-a x+b\) is divided by \(x-1\) and \(x+1\), the remainders are 5 and 19, respectively. If \(f(x)\) is divided by \(x-2\). The remainder is
- A 8
- B 5
- C 10
- D 12
Answer & Solution
Correct Answer
(C) 10
Step-by-step Solution
Detailed explanation
\(f(x)=x^4-2 x^3+3 x^2-a x+b\) Given that, \(f(1)=5\) and \(f(-1)=19\), then \[ \begin{aligned} & f(1)=1-2+3-a+b=2-a+b=5 \\ & \therefore \quad b-a=3 \\ & \text { and } f(-1)=1+2+3+a+b \\ & =b+a+6=19 \\ & \therefore \quad b+a=13 \\ & \end{aligned} \] adding Eqs. (i) and (ii), we…
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