WBJEE · Maths · Quadratic Equation
If \(\alpha, \beta\) are the roots of \(a x^{2}+b x+c=0(a \neq 0)\) and \(\alpha+h, \beta+h\) are the roots of \(p x^{2}+q x+r=0\) \((p \neq 0),\) then the ratio of the squares of their discriminants is
- A \(a^{2}: p^{2}\)
- B \(a: p^{2}\)
- C \(a^{2}: p\)
- D \(a: 2 p\)
Answer & Solution
Correct Answer
(A) \(a^{2}: p^{2}\)
Step-by-step Solution
Detailed explanation
Given, \(\alpha, \beta\) are the roots of \(a x^{2}+b x+c=0\) and \(a+h, \beta+h\) are the roots of \(p x^{2}+q x+r=0\) \(\therefore \quad \alpha+\beta=-\frac{b}{a}, \alpha \beta=\frac{c}{a}\) and \(\alpha+h+\beta+h=-\frac{q}{p},(\alpha+h)(\beta+h)=\frac{r}{p}\) Now,…
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