TS EAMCET · Maths · Quadratic Equation
\(\alpha, \beta, \gamma\) are the roots of the equation \(x^3+3 x^2-10 x-24=0\). If \(\alpha\gt\beta\gt\gamma\) and \(\alpha^3+3 \beta^2-10 \gamma-24=11 k\), then \(k=\)
- A 1
- B 11
- C 5
- D 55
Answer & Solution
Correct Answer
(C) 5
Step-by-step Solution
Detailed explanation
\(x^3+3 x^2-10 x-24=0, \alpha, \beta, \gamma\) are its roots \(x=3\) is one of its root (by hit and trial) On dividing by \((x-3)\), we get \((x-3)\left(x^2+6 x+8\right)=0\) Other roots are factors of \(x^2+6 x+8=(x+4)(x+2)\) i.e.…
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