TS EAMCET · Maths · Quadratic Equation
If the roots of the equation \(4 x^3-12 x^2+11 x+k=0\) are in arithmetic progression, then \(k\) is equal to
- A \(-3\)
- B \(1\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(A) \(-3\)
Step-by-step Solution
Detailed explanation
Since, the roots of the equation \(4 x^3-12 x^2\) \(+11 x+k=0\) are in A.P is \(\alpha-a, \alpha, \alpha+a\) \(\therefore\) Sum of roots, \(\quad 3 \alpha=\frac{12}{4}=3\) \[ \Rightarrow \quad \alpha=1 \] Since, \(\alpha\) is a root, therefore it satisfies the given equation…
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