For what value of m will the quadratic equation (m+1)x^2-(2m+3)x+m+3=0 have two different solutions?
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Answer:
m ∈ (- ∞, - 1)
Step-by-step explanation:
ax² + bx + c = 0
has
one solution, if D = b² - 4ac = 0;
two solutions, if D = b² - 4ac > 0; and
no solutions, if D = b² - 4ac < 0.
(2m + 3)² - 4(m + 3)(m + 1) > 0
4m² + 12m + 9 - 4m² - 16m - 13 > 0
- 4m - 4 > 0
- 4(m + 1) > 0
m + 1 < 0
m < - 1
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