TS EAMCET · Maths · Quadratic Equation
If the roots of the equation \(32 x^3-48 x^2+22 x-3=0\) are in arithmetic progression, then the square of the common difference of the roots is
- A \(\frac{1}{4}\)
- B \(\frac{1}{16}\)
- C \(\frac{1}{9}\)
- D \(\frac{1}{25}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{16}\)
Step-by-step Solution
Detailed explanation
Let the roots be \(a-d, a, a+d\). \(3a = -\frac{-48}{32} = \frac{3}{2} \implies a = \frac{1}{2}\) \(a(a^2-d^2) = -\frac{-3}{32} = \frac{3}{32}\) \(\frac{1}{2}\left(\left(\frac{1}{2}\right)^2 - d^2\right) = \frac{3}{32}\) \(\frac{1}{4} - d^2 = \frac{3}{16}\)…
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