Multiple choice

For what positive value of $m$, the equation $\displaystyle { 12x }^{ 2 }+4\left( m+1 \right) x+3=0$ will have equal roots?

  1. $1$
  2. $4$
  3. $3$
  4. $2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For equal roots, the discriminant b^2 - 4ac must be 0. Here, 16(m+1)^2 - 4(12)(3) = 0. 16(m+1)^2 = 144. (m+1)^2 = 9. m+1 = 3 or -3. Since m is positive, m = 2.

AI explanation

For the equation to have equal roots, the discriminant must be zero. Applying the formula D = b^2 - 4ac to 12x^2 + 4(m+1)x + 3 = 0, we write (4(m+1))^2 - 4(12)(3) = 0. This simplifies to 16(m^2 + 2m + 1) = 144, yielding m^2 + 2m - 8 = 0; factoring this gives (m+4)(m-2) = 0, so the positive value is 2.

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