AP EAMCET · Maths · Quadratic Equation
If \(\alpha\) and \(\beta\) are the roots of the equation \(a x^2+b x+c=0\) and, if \(p x^2+q x+r=0\) has roots \(\frac{1-\alpha}{\alpha}\) and \(\frac{1-\beta}{\beta}\), then \(r\) is equal to
- A \(a+2 b\)
- B \(a+b+c\)
- C \(a b+b c+c a\)
- D \(a b c\)
Answer & Solution
Correct Answer
(B) \(a+b+c\)
Step-by-step Solution
Detailed explanation
Since, \(\alpha, \beta\) are the roots of the equation \(a x^2+b x+c=0\). \(\therefore \quad \alpha+\beta=-\frac{b}{a} \quad \alpha \beta=\frac{c}{a}\) The quadratic equation whose roots are \(\frac{1-\alpha}{\alpha}\) and \(\frac{1-\beta}{\beta}\), is…
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