Multiple choice

Find a quadratic equation, from the equations given below, having same discriminant as $5x^2+2x+1=0$

  1. $-x^2+4x-8$
  2. $x^2+3x-7$
  3. $4x^2-5$
  4. $-2x^2-3x+6$
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A Correct answer
Explanation

The discriminant of 5x^2 + 2x + 1 = 0 is D = b^2 - 4ac = 2^2 - 4(5)(1) = 4 - 20 = -16. For option A, -x^2 + 4x - 8, D = 4^2 - 4(-1)(-8) = 16 - 32 = -16. Since the discriminants match, A is correct.

AI explanation

The discriminant of the equation 5x^2 + 2x + 1 = 0 is calculated as D = 2^2 - 4(5)(1), which gives 4 - 20 = -16. For the equation -x^2 + 4x - 8 = 0, the discriminant is D = 4^2 - 4(-1)(-8), which equals 16 - 32 = -16. Since both equations have the exact same discriminant value, the matching equation is -x^2 + 4x - 8.

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