AP EAMCET · Maths · Quadratic Equation
If \(\alpha\) and \(\beta\) are the roots of the equation \(a^2+b x+c=0\), then the equation whose roots are \(\alpha+\beta\) and \(\frac{1}{\alpha}+\frac{1}{\beta}\) is
- A \(a c x^2-(a b+b c) x+b^2=0\)
- B \(a c x^2+(a b+b c) x-b^2=0\)
- C \(a c x^2+(a b+b c) x+b^2=0\)
- D \(a c x^2-(a b+b c) x-b^2=0\)
Answer & Solution
Correct Answer
(C) \(a c x^2+(a b+b c) x+b^2=0\)
Step-by-step Solution
Detailed explanation
Given : \(\alpha\) and \(\beta\) are roots of the equation \(a x^2+b x+c=0\) \(\therefore \quad \alpha+\beta=-\frac{b}{a}\) and \(\alpha \beta=\frac{c}{a}\) \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}=\frac{-\frac{b}{a}}{\frac{c}{a}}=-\frac{b}{c}\) given…
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