AP EAMCET · Maths · Quadratic Equation
Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation \(a x^2+b x+c=0\). Observe the lists given below
The correct match of List-I from List-II is
(i) (ii) (iii) (iv)
- A \(\begin{array}{llll}\mathrm{E} & \mathrm{B} & \mathrm{D} & \mathrm{F}\end{array}\)
- B \(\begin{array}{llll}\mathrm{E} & \mathrm{B} & \mathrm{A} & \mathrm{D}\end{array}\)
- C \(\begin{array}{llll}\mathrm{E} & \mathrm{D} & \mathrm{B} & \mathrm{F}\end{array}\)
- D E \(\quad\) B \(\quad\) D \(\quad\) A
Answer & Solution
Correct Answer
(D) E \(\quad\) B \(\quad\) D \(\quad\) A
Step-by-step Solution
Detailed explanation
Using the condition that the roots of \(a x^2+b x+c=0\) may be in the ratio \(m: n\) is \(m n b^2=a c(m+n)^2\). (i) If the roots are \(\alpha=\beta\), then \[ \begin{aligned} \alpha \cdot \alpha b^2 & =a c(\alpha+\alpha)^2 \\ \Rightarrow \quad b^2 & =4 a c \end{aligned} \]…
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