TS EAMCET · Maths · Quadratic Equation
If \(\alpha+\beta=-2\) and \(\alpha^3+\beta^3=-56\), then the quadratic equation whose roots are \(\alpha\) and \(\beta\) is
- A \(x^2+2 x-16=0\)
- B \(x^2+2 x+15=0\)
- C \(x^2+2 x-12=0\)
- D \(x^2+2 x-8=0\)
Answer & Solution
Correct Answer
(D) \(x^2+2 x-8=0\)
Step-by-step Solution
Detailed explanation
Given that, \(\alpha+\beta=-2\) and \(\alpha^3+\beta^3=-56\) \[ \begin{array}{rlrl} \Rightarrow & & (\alpha+\beta)\left(\alpha^2+\beta^2-\alpha \beta\right) & =-56 \\ \Rightarrow & \alpha^2+\beta^2-\alpha \beta & =28 \end{array} \]…
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