Consider the quadratic equation x^2-6x=-1 a: what is the value of the discriminant? explain. b: how many solutions does the quadratic equation have and are those solutions rational irrational or nonreal? explain. c: if the quadratic equation has real solutions, what are the solutions? explain. estimate irrational solutions to the nearest tenth.

The discriminant is the part under the radical sign in the quadratic formula for a quadratic of the form ax^2+bx+c.

The quadratic formula is:

x=(-b±√(b^2-4ac))/(2a), the discriminant is then:

b^2-4ac

You equation is x^2-6x+1 so its discriminant is:

36-4=32



So you will have two real irrational solutions.

In general if the discriminant is:

d<0, there are no real solutions (but there are two imaginary or nonreal ones)

d=0, there is one real solution

d>0, there are two real solutions.

...

x=(6±√32)/2

x=(6±√(16*2)/2

x=(6±4√2)/2

x=3±2√2

x≈0.2 and 5.8  (to nearest tenths)