TS EAMCET · Maths · Quadratic Equation
If the roots of \(x^3+a x^2+b x+c=0\) are in arithmetic progression with common difference 1 , then
- A \(9 c=a(b-2)\)
- B \(9 c=a(2-b)\)
- C \(9 c-a^2(b-2)=0\)
- D \(9 c-a^2(2-b)=0\)
Answer & Solution
Correct Answer
(A) \(9 c=a(b-2)\)
Step-by-step Solution
Detailed explanation
Let the roots of \(x^3+a x^2+b x+c=0\) are \(\alpha-1, \alpha, \alpha+1\) as roots are in AP with common difference 1 . Now, sum of roots \(=3 \alpha=-a\) \(\ldots(\mathrm{i})\) Sum of product of roots taking two at a time…
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