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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

  1. A \(x^2+2 x-16=0\)
  2. B \(x^2+2 x+15=0\)
  3. C \(x^2+2 x-12=0\)
  4. D \(x^2+2 x-8=0\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(x^2+2 x-8=0\)

Step-by-step Solution

Detailed explanation

Given that, \(\alpha+\beta=-2\) and \(\alpha^3+\beta^3=-56\) \[ \begin{array}{rlrl} \Rightarrow & & (\alpha+\beta)\left(\alpha^2+\beta^2-\alpha \beta\right) & =-56 \\ \Rightarrow & \alpha^2+\beta^2-\alpha \beta & =28 \end{array} \]…