Real analysis

Find all values of m for which the quadratic equation 2x2 + 3 x - m + 2 = 0 have two distinct real solutions.

Solutions

Expert Solution

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

Nipun Maity answered 2 years ago

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