AP EAMCET · Maths · Quadratic Equation
The polynomial equation of degree 5 whose roots are the roots of the equation \(x^5-3 x^4-x^3+11 x^2-12 x+4=0\) each increased by 2, is
- A \(x^5-13 x^4+63 x^3-135 x^2-108 x=0\)
- B \(x^5-13 x^4+63 x^3+135 x^2+108 x=0\)
- C \(x^5-13 x^4+63 x^3-135 x^2+108 x=0\)
- D \(x^5-13 x^4-63 x^3-135 x^2-108=0\)
Answer & Solution
Correct Answer
(C) \(x^5-13 x^4+63 x^3-135 x^2+108 x=0\)
Step-by-step Solution
Detailed explanation
Let the given polynomial be \(P(x) = x^5-3 x^4-x^3+11 x^2-12 x+4\). If the roots are increased by 2, the new polynomial is \(P(x-2)=0\). Substitute \(x \leftarrow x-2\): \((x-2)^5 - 3(x-2)^4 - (x-2)^3 + 11(x-2)^2 - 12(x-2) + 4 = 0\) Expanding and collecting terms:…
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