Use the discriminant to determine how many and what kind of solutions the quadratic equation x^2-x=1 has.
a)one real solution
b)no real or complex solutions
c)two complex (nonreal) solutions
d) two real solutions
To determine the number and type of solutions, we can use the discriminant formula. The discriminant is given by b^2-4ac, where a, b, and c are the coefficients of the quadratic equation ax^2+bx+c=0.
In the given equation x^2-x=1, we have a=1, b=-1, and c=-1. Therefore, the discriminant is calculated as (-1)^2-4(1)(-1) = 1+4 = 5.
Since the discriminant is positive (5), the equation has two real solutions. Therefore, the answer is d) two real solutions.