AP EAMCET · Maths · Quadratic Equation
If the roots of the equation \(x^3-7 x^2+14 x-8=0\) are in geometric progression, then the difference between the largest and the smallest roots is
- A 4
- B 2
- C \(\frac{1}{2}\)
- D 3
Answer & Solution
Correct Answer
(D) 3
Step-by-step Solution
Detailed explanation
Given equation, \(x^3-7 x^2+14 x-8=0\) Let the roots of this equation are \(\frac{a}{r}, a, a r\). Then, we get Sum of roots \(=7\) \(\frac{a}{r}+a+a r=7 ...(i)\) Product of consecutive roots \(=14\) \(\frac{a}{r} \cdot a+a \cdot a r+a r \cdot \frac{a}{r}=14 ...(ii)\) Product of…
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