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CA Foundation · Quantitative Aptitude · Equations

How many real roots does the biquadratic equation x⁴ − 5x² + 4 = 0 have?

The equation has four real roots. Substituting y = x² gives y² − 5y + 4 = 0, so y = 1 or 4. Hence x = ±1 and ±2, which are four distinct real values.

  1. A2
  2. B3
  3. C4Correct
  4. D0

Explanation

Put y = x², giving y² − 5y + 4 = 0, so (y − 1)(y − 4) = 0 and y = 1 or 4. Then x = ±1 or ±2, which gives four distinct real roots. Answering 2 would result from taking only positive values of x.

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