AP EAMCET · Maths · Quadratic Equation
If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-4 x+5=0\), then the quadratic equation whose roots are \(\alpha^2+\beta\) and \(\alpha+\beta^2\) is
- A \(x^2+10 x+34=0\)
- B \(x^2-10 x+34=0\)
- C \(x^2-10 x-34=0\)
- D \(x^2+10 x-34=0\)
Answer & Solution
Correct Answer
(B) \(x^2-10 x+34=0\)
Step-by-step Solution
Detailed explanation
Since, \(\alpha\) and \(\beta\) are roots of the quadratic equation \[ x^2-4 x+5=0 \] So, \(\alpha+\beta=4\) and \(\alpha \beta=5 ...(i)\) Now, \(\left(\alpha^2+\beta\right)+\left(\alpha+\beta^2\right)=\left(\alpha^2+\beta^2\right)+(\alpha+\beta)\)…
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