Loliateyourcat
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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.

Respuesta :

irspow
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)

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