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Bamboozled

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Quadratic Equations

Hey, I'm confused by this question, I'm not even sure what it is asking me to do?

1. Given that the following expressions are positive for all real values of x, find in each case the set of possible values of a.
(a) x²+a+a²
(b) x²+ax+a²
(c) x²-2ax+3a
(d) ax²+2ax+a²

The next question doesn't seem to be right. I don't get the values to be of the same sign...

2. Find the set of values of k for which the roots of the equation x²+kx-k+3=0 are real and of the same sign.

And finally, what do I actually DO with this question? Do I need to substitute in numbers or something?

3. Given that y=px²+2qx+r, show that y will have teh same sign for all real values of x if and only if q² < pr.

Thank you very much in advace.

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: Quadratic Equations

2. Find the set of values of k for which the roots of the equation x²+kx-k+3=0 are real and of the same sign.

k - 2 = 0
k = 2
or
k + 6 = 0
k = -6

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Nehushtan

Member

Registered: 2013-03-09

Posts: 957

Re: Quadratic Equations

Monox's solution is wrong; that solution is only for the case when the roots are real and equal.

2. Find the set of values of k for which the roots of the equation x²+kx-k+3=0 are real and of the same sign.

For real roots we require

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[*]

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[/list]

For the roots to be of the same sign, their product must be positive. So we want

[list=*]
[*]

[/*]
[/list]

Hence the set of values we want is

[list=*]
[*]

[/*]
[/list]

Last edited by Nehushtan (2016-02-03 18:54:20)

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