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jacks

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biquadratic equation

How many Negative roots of the equation

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: biquadratic equation

hi jacks,

If you differentiate you get

So if we knew it's roots we'd know where the turning points of the quartic are;  but it doesn't solve readily.

So differentiate again

This quadratic has two roots, one negative and one positive, so the cubic has two turning points; the negative one is a maximum and the positive one is a minimum.

Substitute the negative one and you'll find this maximum is a negative value, so the cubic only crosses the x axis once, at a point after the positive root of the quadratic.

That crossing point means the quartic has only one turning point and it's at a positive value of x.

When x = o the quartic = 4, => it never crosses the x axis in negative values.

The graphs below may help to show this more clearly.

Bob

Last edited by Bob (2011-11-13 20:45:49)

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