polynomial (1 Viewer)

alexchen17 · Feb 13, 2017

Please help me on question c thanks

He-Mann · Feb 13, 2017

Hints:

a) Factor Theorem

b) Factor Theorem

c) Differentiation and Factor Theorem

integral95 · Feb 13, 2017

This is where you consider the product of roots, which is 1.

$$Since$ \ \alpha \ $is a multiple root, then it must AT LEAST have a multiplicity of 2, we're also given that $ \frac{1}{\alpha} \ $ is a root, so if $ \ \alpha $ \ \ has a multiplicity of 3, then the roots would be $ \alpha , \alpha , \alpha , \frac{1}{\alpha} $ which would imply that $ \ \alpha =+-1$ , \ \ but we know that can't happen from part a). Therefore $\alpha$ only has a multiplicity of 2. Therefore we know that 3 of the roots are $\alpha , \alpha,\frac{1}{\alpha}$. The fourth root must also be $\frac{1}{\alpha}$ to satisfy the product of roots.$

integral95 · Feb 13, 2017

19KANguy · Feb 24, 2017

If a and b are roots of the equation x^2 + 8x -5=0, find the quadratic equation whose roots are a/b and b/a

He-Mann · Feb 25, 2017

19KANguy said:
If a and b are roots of the equation x^2 + 8x -5=0, find the quadratic equation whose roots are a/b and b/a

Some hints.

$\frac{a}{b} + \frac{b}{a} = \frac{a^2 + b^2}{ab} = \frac{74}{-5}$

$\frac{a}{b} \cdot \frac{b}{a} = 1$

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polynomial (1 Viewer)

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