TS EAMCET · Maths · Quadratic Equation
The equation \(16 x^4+16 x^3-4 x-1=0\) has a multiple root. If \(\alpha, \beta, \gamma, \delta\) are the roots of this equation, then \(\frac{1}{\alpha^4}+\frac{1}{\beta^4}+\frac{1}{\gamma^4}+\frac{1}{\delta^4}=\)
- A \(\frac{1}{64}\)
- B \(\frac{1}{32}\)
- C \(32\)
- D \(64\)
Answer & Solution
Correct Answer
(D) \(64\)
Step-by-step Solution
Detailed explanation
Given: \(16 x^4+16 x^3-4 x-1=0=f(x)\) has a multiple root. Let \(\alpha=\beta\) be the multiple root. Since \(\alpha\) is root of \(f(x) \quad \therefore f(\alpha)=0\) \(\Rightarrow 16 \alpha^4+16 \alpha^3-4 \alpha-1=0\) ...(i) As \(\alpha\) is multiple root…
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