Multiple choice

If the equation x2-(2+m)x+(-m2-4m-4)=0 has coincident roots then

  1. m = 0, m = 1

  2. m = 2, m = 2

  3. m = -2 , m = -2

  4. m = 6 , m = 1
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C Correct answer
Explanation

Coincident roots require the discriminant to be zero. Here the discriminant simplifies to 5(m + 2)^2, so m = -2.

AI explanation

A quadratic equation has coincident roots when its discriminant equals zero. For x2 - (2 + m)x + (-m2 - 4m - 4) = 0, the discriminant is (2 + m)2 - 4(-m2 - 4m - 4), which simplifies to 4 + 4m + m2 + 4m2 + 16m + 16. Setting this equal to zero gives 5m2 + 20m + 20 = 0, and dividing by 5 yields m2 + 4m + 4 = 0. Factoring this gives (m + 2)2 = 0, so the only solution is m = -2.

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