AP EAMCET · Maths · Quadratic Equation
When the roots of \(x^3+\alpha x^2+\beta x+6=0\) are increased by 1, if one of the resultant values is the least root of \(x^4-6 x^3+11 x^2-6 x=0\), then
- A \(\alpha-\beta+5=0\)
- B \(\alpha+\beta+7=0\)
- C \(2 \alpha+\beta+7=0\)
- D \(2 \alpha+3 \beta-1=0\)
Answer & Solution
Correct Answer
(A) \(\alpha-\beta+5=0\)
Step-by-step Solution
Detailed explanation
\(x^4-6 x^3+11 x^2-6 x=0 \implies x(x^3-6 x^2+11 x-6)=0\) \(x(x-1)(x-2)(x-3)=0\) Roots: \(0, 1, 2, 3\). Least root: \(0\). Let \(r\) be a root of \(x^3+\alpha x^2+\beta x+6=0\). One resultant value is \(r+1\). \(r+1=0 \implies r=-1\). Substitute \(x=-1\) into…
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