TS EAMCET · Maths · Quadratic Equation
For the equation \(x^4+x^3-4 x^2+x-1=0\) the ratio of the sum of the squares of all the roots to the product of the distinct roots is
- A \(1: 4\)
- B \(3: 5\)
- C \(9: 1\)
- D \(4: 3\)
Answer & Solution
Correct Answer
(C) \(9: 1\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } \begin{aligned} p(x) & =x^4+x^3-4 x^2+x-1 \\ & =(x-1)\left(x^3+2 x^2-2 x-1\right) \\ & =(x-1)(x-1)\left(x^2+3 x+1\right) \\ =(x-1) & (x-1)\left[x-\left(\frac{-3+\sqrt{5}}{2}\right)\right]\left[x-\left(\frac{-3-\sqrt{5}}{2}\right)\right]…
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