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2005 P2 Q11 - HSN forum

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2005 P2 Q11


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#1 Hev

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Posted 18 May 2006 - 03:36 PM

11 b.

[x=-1 in the solution of the cubic equation x^3 + px^2 +px +1 = 0]

Hence find the range of values for p for which all the roots of the cubic equations are real. (7 marks)

Can anyone help me please? I'm beyond useless at these questions!
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#2 George

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Posted 18 May 2006 - 03:45 PM

OK, since x= -1 is a root, you can factorise to get (x+1)(x^2 + (p-1)x + 1)=0.

The roots of that equation will all be real if the roots of x^2 + (p-1)x + 1=0 are both real.

Now, you can have a look at the examples in the Polynomials and Quadratics notes - sections 2 and 6 should be helpful smile.gif

#3 Hev

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Posted 18 May 2006 - 03:50 PM

Thanks, i just didn't even know where to start!
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#4 will_789

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Posted 18 May 2006 - 03:58 PM

Now use the discriminant
b power2.gif -4ac greaterorequal.gif 0





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