AP EAMCET · Maths · Quadratic Equation
If \(\alpha \neq 0\) and zero are the roots of the equation \(x^2-5 k x+\left(6 k^2-2 k\right)=0\), then \(\alpha=\)
- A \(\frac{1}{3}\)
- B 1
- C \(\frac{5}{3}\)
- D 5
Answer & Solution
Correct Answer
(C) \(\frac{5}{3}\)
Step-by-step Solution
Detailed explanation
\(\alpha + 0 = 5k \implies \alpha = 5k\) \(\alpha \cdot 0 = 6k^2 - 2k \implies 6k^2 - 2k = 0\) \(2k(3k - 1) = 0\) \(k = 0\) or \(k = \frac{1}{3}\) Since \(\alpha \neq 0\), \(k \neq 0\). Thus \(k = \frac{1}{3}\) \(\alpha = 5 \left(\frac{1}{3}\right) = \frac{5}{3}\)
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