Multiple choice

Solve the following quadratic equations and choose the correct answer accordingly. I. x2 - 2x - 3 = 0 II. y2 + 5y + 6 = 0

  1. x > y

  2. x < y

  3. x ≤ y

  4. x ≥ y

  5. x = y or No relation can be established.
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A Correct answer
Explanation

I. x^2 - 2x - 3 = 0 => (x-3)(x+1) = 0 => x = 3, -1. II. y^2 + 5y + 6 = 0 => (y+2)(y+3) = 0 => y = -2, -3. Comparing roots: 3 > -2, 3 > -3, -1 > -2, -1 > -3. In all cases, x > y.

AI explanation

Factoring the first equation x2 - 2x - 3 = 0 gives (x - 3)(x + 1) = 0, so the roots for x are 3 and -1. Factoring the second equation y2 + 5y + 6 = 0 gives (y + 2)(y + 3) = 0, so the roots for y are -2 and -3. Comparing these values shows that both roots of x are greater than both roots of y, meaning x > y.

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