AP EAMCET · Maths · Quadratic Equation
If one of the roots of the equation \(x^2+p x+q=0\) is equal to the square of the other then
- A \(p\left(q^2-3 p\right)=q(p-1)\)
- B \(p\left(3 p-q^2\right)=p(p+1)\)
- C \(p\left(3 q-p^2\right)=q(q-1)\)
- D \(p\left(3 q-p^2\right)=q(q+1)\)
Answer & Solution
Correct Answer
(D) \(p\left(3 q-p^2\right)=q(q+1)\)
Step-by-step Solution
Detailed explanation
Given equation \(x^2+p x+q=0\) ...(i) On comparing with \(a x^2+b x+c=0\) \(a=1, b=p, c=q\) Let \(\alpha, \beta\) are the roots of Eq. (i) and given that \(\alpha=\beta^2\) \(\therefore \quad \alpha+\beta=\frac{-b}{a}=-p\) and \(\alpha \beta=\frac{c}{a}=q\)…
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