Question

Find all values of m for which the equation has two real solutions.
3x² + 7x - (m + 1) = 0

Answer 1

This is the answer here

Answer 2

• m > - 5 1/12

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Given is the quadratic equation.

A quadratic equation has two real solutions if the discriminant is positive.

Set inequality and solve for m:

• D = b² - 4ac, where a = 3, b = 7, c = - (m + 1)
• D = 7² + 4*3*(m + 1)

• 7² + 4*3*(m + 1) > 0
• 49 + 12m + 12 > 0
• 12m + 61 > 0
• 12m > - 61
• m > - 61/12
• m > - 5 1/12