AP EAMCET · Maths · Quadratic Equation
If \(\alpha\) is a repeated root of multiplicity 2 of the equation \(18 x^3-33 x^2+20 x-4=0\), then
- A \(3 \alpha^2-8 \alpha+4=0\)
- B \(3 \alpha^2+8 \alpha+4=0\)
- C \(3 \alpha^2-\alpha-4=0\)
- D \(3 \alpha^2+2 \alpha-4=0\)
Answer & Solution
Correct Answer
(A) \(3 \alpha^2-8 \alpha+4=0\)
Step-by-step Solution
Detailed explanation
\(P'(x) = 54x^2 - 66x + 20\) Since \(\alpha\) is a repeated root, \(P'(\alpha) = 0\). \(54\alpha^2 - 66\alpha + 20 = 0\) \(27\alpha^2 - 33\alpha + 10 = 0\) \(\alpha = \frac{33 \pm \sqrt{(-33)^2 - 4(27)(10)}}{2(27)} = \frac{33 \pm \sqrt{1089 - 1080}}{54} = \frac{33 \pm 3}{54}\)…
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