AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^3+3 x^2+4 x\) \(+5=0\), then the cubic equation whose roots are \(1+4 \alpha\), \(1+4 \beta\) and \(1+4 \gamma\) is
- A \(x^3+9 x^2-21 x+267=0\)
- B \(x^3+9 x^2+43 x+267=0\)
- C \(x^3+9 x^2+41 x+267=0\)
- D \(x^3+9 x^2+43 x+267=0\)
Answer & Solution
Correct Answer
(D) \(x^3+9 x^2+43 x+267=0\)
Step-by-step Solution
Detailed explanation
\(\alpha, \beta, \gamma\) are roots of \(x^3+3 x^2+4 x+5=0\) \(\alpha+\beta+\gamma=-3\) ...(i) \(\alpha \beta+\beta \gamma+\gamma \alpha=4\) ...(ii) \(\alpha \beta \gamma=-5\) ...(iii)…
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