AP EAMCET · Maths · Quadratic Equation
Find the remainder when \(x^4-11 x^3+44 x^2-76 x+48\) is divided by \(x^2-7 x+12\).
- A 0
- B 1
- C \(x^2-4 x+4\)
- D \(x^2+4 x-4\)
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
\( x^2-7 x+12 = (x-3)(x-4) \) \( P(3) = (3)^4 - 11(3)^3 + 44(3)^2 - 76(3) + 48 = 81 - 297 + 396 - 228 + 48 = 0 \) \( P(4) = (4)^4 - 11(4)^3 + 44(4)^2 - 76(4) + 48 = 256 - 704 + 704 - 304 + 48 = 0 \) The remainder is \(0\).
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