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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2022 · Mathematics · Quadratic Equation

Let p, q(p > q) be the roots of the quadratic equation x^2+b x+c=0...

Let p,q(p>q)p, q(p > q) be the roots of the quadratic equation x2+bx+c=0x^2+b x+c=0 where c>0c > 0. If p2+q2−11pq=0p^2+q^2-11 p q=0, then what is p−qp-q equal to?

Options

  1. A3c3 \sqrt{c}
  2. B3c3 c
  3. C9c9 \sqrt{c}
  4. D9c9 c

Correct answer

A. 3c3 \sqrt{c}

Step-by-step solution

Given that roots of x2+bx+c=0x^2+b x+c=0 are pandqp and q. ∴p+q=−b and pq=cGiventhat\therefore \quad p+q=-b \text{ and } p q=c Given thatp2+q2−11pq=0⇒(p+q)2−13pq=0⇒b2−13c=0\begin{aligned}& p^2+q^2-11 p q=0 \\ & \Rightarrow(p+q)^2-13 p q=0 \\ & \Rightarrow b^2-13 c=0 \end{aligned}⇒b2−13c\Rightarrow b^2-13 c...(i)  Now (p−q)2=(p+q)2−4pq=b2−4c=13c−4c=9cp−q=3c\begin{aligned} & \text{ Now }(p-q)^2=(p+q)^2-4 p q \\ & =b^2-4 c=13 c-4 c=9 c \\ & p-q=3 \sqrt{c} \end{aligned}$ [from (i)]
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