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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2019 · Mathematics · Quadratic Equation

If both p and q belong to the set (1,2,3,4) , then how many...

If both pp and qq belong to the set (1,2,3,4)(1,2,3,4), then how many equations of the form px2+qx+1=0p x^2+q x+1=0 will have real roots?

Options

  1. A12
  2. B10
  3. C7
  4. D6

Correct answer

C. 7

Step-by-step solution

p,q∈{1,2,3,4}p, q \in\{1,2,3,4\} For real roots q2≥4pq^2 \geq 4 p If q=1,p=ϕq=1, p=\phi If q=2,p=1q=2, p=1 If q=3,p=1,2q=3, p=1,2 If q=4,p=1,2,3,4∴7q=4, p=1,2,3,4\therefore 7 such pairs exist.
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