Multiple choice

The equation $\displaystyle \left ( m+1 \right )x^{2}+2mx+5x+m+3=0$ has equal roots Find the value of m

  1. -11/4

  2. -13/4

  3. -15/4

  4. -17/4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0 to have equal roots, the discriminant b^2 - 4ac must be 0. Here, a = (m+1), b = (2m+5), c = (m+3). (2m+5)^2 - 4(m+1)(m+3) = 0. 4m^2 + 20m + 25 - 4(m^2 + 4m + 3) = 0. 4m^2 + 20m + 25 - 4m^2 - 16m - 12 = 0. 4m + 13 = 0, so m = -13/4.

AI explanation

Rewrite the equation in standard form as (m + 1)x^2 + (2m + 5)x + (m + 3) = 0. For the equation to have equal roots, the discriminant must be zero, so (2m + 5)^2 - 4(m + 1)(m + 3) = 0. Expanding both terms gives 4m^2 + 20m + 25 - (4m^2 + 16m + 12) = 0. Combining like terms results in 4m + 13 = 0, which gives m = -13/4.

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