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20 December, 19:43

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.

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  1. 20 December, 20:03
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    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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