Exercise 47 Page 196

Let's recall the definition of the discriminant. 2 &Quadratic equation: && ax^2+ bx+ c=0 &Discriminant:&& b^2-4 a c This is useful because the sign of the discriminant tells us the number of real solutions of a quadratic equation.

Let's identify the coefficients in the equation given in the question. x^2+x+m+1= 1x^2+ 1x+( m+1) We see that a= 1, b= 1, and c= m+1. Let's use these coefficients to find the discriminant.

According to the table above, the discriminant must be 0 if the equation has one solution.

The only value for which the given equation has exactly one solution is m=-0.75.