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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2021 · Mathematics · Quadratic Equation

If p and q are the non-zero roots of the equation x^2+p x+q=0 ,...

If pp and qq are the non-zero roots of the equation x2+px+q=0x^2+p x+q=0, then how many possible values can qq have?

Options

  1. ANil
  2. BOne
  3. CTwo
  4. DThree

Correct answer

B. One

Step-by-step solution

Since pandqp and q are the non-zero roots of the equation x2+px+q=0 then p2+p2+q=0\begin{aligned} & x^2+p x+q=0 \text{ then } \\ & p^2+p^2+q=0 \end{aligned}\Rightarrow q=2 p^2.....(i).....(i) and q2+pq+q=0⇒q(q+p+1)=0\begin{aligned} & \text{ and } q^2+p q+q=0 \\ & \Rightarrow q(q+p+1)=0\end{aligned}⇒q+p+1=0[∴q≠0]⇒−2p2+p+1=0[from(i)]\Rightarrow q+p+1=0 \quad[\therefore q \neq 0]\Rightarrow-2 p^2+p+1=0 \quad [\mathrm{from(i)}]⇒2p2−p−1=0⇒(p−1)(2p+1)=0p=1,p=−12q=−2,−12\begin{aligned} \Rightarrow & 2 p^2-p-1=0 \\ \Rightarrow & (p-1)(2 p+1)=0 \\ & p=1, \mathrm{p}=-\frac{1}{2} \\ & q=-2,-\frac{1}{2}\end{aligned}$$
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