WBJEE · Maths · Quadratic Equation
If \(\alpha, \beta\) are the roots of the quadratic equation \(x^{2}+a x+b=0,(b \neq 0),\) then the quadratic equation whose roots are \(\alpha-\frac{1}{\beta}, \beta-\frac{1}{\alpha},\) is
- A \(a x^{2}+a(b-1) x+(a-1)^{2}=0\)
- B \(b x^{2}+a(b-1) x+(b-1)^{2}=0\)
- C \(x^{2}+a x+b v=0\)
- D \(a b x^{2}+b x+a=0\)
Answer & Solution
Correct Answer
(B) \(b x^{2}+a(b-1) x+(b-1)^{2}=0\)
Step-by-step Solution
Detailed explanation
Given equation is, \(x^{2}+a x+b=0,(b \neq 0)\) its roots are \(\alpha\) and \(\beta\). Then, sum of roots \(=\alpha+\beta=-a\) Product of roots \(=\alpha \cdot \beta=b\) Now,…
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