Question

In: Advanced Math

real analysis

Find all values of m for which the quadratic equation x²+ 2 x - 2 m = 0 have no real solutions.

Solutions

Expert Solution

The type and number of solutions is determined by the sign of the discriminant of the quadratic equation. The discriminant of the given equation is equal to

22 - 4(1)(-2m) = 4 + 8m

A quadratic equation has no solutions if it discriminant is negative. Hence

4 + 8m < 0

Solve the above inequality to obtain

m < -1/2

The given quadratic equation has no real solutions for all values of m such that m < -1/2

m<-1/2

Nipun Maity answered 2 years ago
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