AP EAMCET · Maths · Quadratic Equation
If the equation \(x^5-3 x^4-5 x^3+27 x^2-32 x+12=0\) has repeated roots, then the prime number that divides the non-repeated root of this equation is
- A \(7\)
- B \(5\)
- C \(3\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
\(P(x) = x^5-3 x^4-5 x^3+27 x^2-32 x+12\) \(P(2) = 2^5-3(2^4)-5(2^3)+27(2^2)-32(2)+12 = 32-48-40+108-64+12 = 0\) \(P'(x) = 5x^4 - 12x^3 - 15x^2 + 54x - 32\) \(P'(2) = 5(2^4) - 12(2^3) - 15(2^2) + 54(2) - 32 = 80-96-60+108-32 = 0\) \(P(x) = (x-2)^2(x^3+x^2-5x+3)\)…
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