Multiple choice

If the equation $x^2 +2 (k+ 1)x + 9 = 0$ has equal roots, then the value of $k$ is

  1. $2$
  2. $3$
  3. $4$
  4. $5$
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A Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0 to have equal roots, the discriminant D = b^2 - 4ac must be zero. Here, (2(k+1))^2 - 4(1)(9) = 0, which simplifies to 4(k+1)^2 = 36, so (k+1)^2 = 9. Thus, k+1 = 3 or k+1 = -3, giving k = 2 or k = -4.

AI explanation

For the quadratic equation to have equal roots, the discriminant must be zero, meaning b squared minus 4 times a times c equals zero. Substituting the values a = 1, b = 2(k + 1) and c = 9 gives the equation (2(k + 1)) squared minus 4 multiplied by 1 multiplied by 9 equals 0. Simplifying this yields 4 times the quantity (k plus 1) squared equals 36, which means (k + 1) squared equals 9. Taking the square root of both sides gives k + 1 equals plus or minus 3, resulting in k = 2 or k = -4, meaning the value of k from the provided choices is 2.

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