AP EAMCET · Maths · Quadratic Equation
Let \(f(x)\) be a polynomial and \(a, b\) be distinct real numbers. Then the remainder in the division of \(f(x)\) by \((x-a)(x-b)\) is
- A \(\frac{(x-a) f(a)-(x-b) f(b)}{a-b}\)
- B \(\frac{(x-a) f(b)-(x-b) f(a)}{a-b}\)
- C \(\frac{(x-a) f(b)-(x-b) f(a)}{b-a}\)
- D \(\frac{(x-a) f(a)-(x-b) f(b)}{b-a}\)
Answer & Solution
Correct Answer
(C) \(\frac{(x-a) f(b)-(x-b) f(a)}{b-a}\)
Step-by-step Solution
Detailed explanation
Let \(f(x)=(x-a)(x-b) \cdot q(x)+r(x)\) Let \(r(x)=\alpha x+\beta \quad[\because \operatorname{deg} r(x) < \operatorname{deg}\). of divisor]…
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