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GATE 2014 CS (CS1) – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

The roots of $ax^2+bx+c=0$ are real and positive, with real a, b, c. Then $ax^2+b|x|+c=0$ has ______.

  1. no roots
  2. 2 real roots
  3. 3 real roots
  4. 4 real roots

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Show answer and explanation

Correct answer: (D) 4 real roots

Explanation

Let the two positive roots of ay²+by+c=0 be r₁,r₂. Setting y=|x| yields x=±r₁,±r₂, giving **four roots, D**, under the intended assumption that the positive roots are distinct. If the original has a repeated positive root, there are only two distinct roots; the source does not explicitly exclude that case.