VioletPhillippo
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Hiya,

I've been practising some roots of equations questions and I've become stuck on this question as I've never done one where the changes to the roots are different.
1. Cubic equation: 3z^3 + pz^2+qz+15=0
Roots: alpha, 1-2 (alpha), and 1/alpha.
Find the roots and the value of p & q

I'm also stuck on a more basic quadratic one. Z^2-5z+1 has roots alpha and beta.
Find quadratic equation with roots: 2 alpha +1, 2 beta + 1.

And finally an indentity question:
X^2-x+3= L (x-1)^2+M (x-1)(×+2)+N (x+2)^2
Find the values of the letters.

Any help would be much appreciated
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ghostwalker
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Report 5 years ago
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(Original post by VioletPhillippo)
Hiya,

I've been practising some roots of equations questions and I've become stuck on this question as I've never done one where the changes to the roots are different.
1. Cubic equation: 3z^3 + pz^2+qz+15=0
Roots: alpha, 1-2 (alpha), and 1/alpha.
Find the roots and the value of p & q
For this first one, consider the product of the three roots: What is it in terms of alpha, and what is it in terms of your polynomial.
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ghostwalker
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(Original post by VioletPhillippo)
I'm also stuck on a more basic quadratic one. Z^2-5z+1 has roots alpha and beta.
Find quadratic equation with roots: 2 alpha +1, 2 beta + 1.
From your initial quadratic, you know what \alpha+\beta and [latex]\alpha\beta[/latex are......(1)

For your new equations work out the sum and product of your new roots and use (1) to evaluate them.

And finally an indentity question:
X^2-x+3= L (x-1)^2+M (x-1)(×+2)+N (x+2)^2
Find the values of the letters.

Any help would be much appreciated
Expand the brackets, group the terms by the powers of x, and equate coefficients.
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