In: Advanced Math
Find all values of m for which the quadratic equation 2x2 + 3 x - m + 2 = 0 have two distinct real solutions.
The discriminant of the given equation is equal to
32 - 4(2)(- m + 2) = 9 + 8m - 16 = -7 + 8m
A quadratic equation has two distinct real solutions if it discriminant is positive. Hence
-7 + 8m > 0
Solve the above inequality to obtain
m > 7 / 8
The given quadratic equation has two distinct real solutions for all values of m such that m > 7 / 8
m>7/8