Polynomials Question (1 Viewer)

boredofstudiesuser1 · Mar 15, 2017

For the polynomial ax^3+15x^2-cx-72 :
2 of its roots are: -3 & 2

Find the 3rd root.

integral95 · Mar 15, 2017

You could only consider the sum of roots and the product of roots of the polynomial, which fortunately is enough.

$$Let the roots be$ \ \ \alpha, \ 2 \ , 3. $ Product of roots gives $ \\ \\ \frac{72}{a} = (-3)(2)(\alpha) \Rightarrow \\ \\ a. \alpha = -12 \ \ (1)$

$$ Sum of roots gives $ \\ \\ -\frac{15}{a} = \alpha - 3 + 2 \Rightarrow -15 + a = a.\alpha =-12 \ \ \ $from$ \ \ (1)$

So you get a = 3 and alpha = -4 with simple algebra

boredofstudiesuser1 · Mar 15, 2017

integral95 said:
You could only consider the sum of roots and the product of roots of the polynomial, which fortunately is enough.

$$Let the roots be$ \ \ \alpha, \ 2 \ , 3 $ Product of roots gives $ \\ \\ \frac{72}{a} = (-3)(2)(\alpha) \Rightarrow \\ \\ a. \alpha = -12 \ \ (1)$

$$ Sum of roots gives $ -\frac{15}{a} = \alpha - 3 + 2 \Rightarrow -15 + a = a.\alpha =-12 \ \ \ $from$ \ \ (1)$

So you get a = 3 and alpha = -4 with simple algebra

Oh great! This is what I got.

Thanks for the clarification

maths methods · Mar 20, 2017

Is 3U maths like vce specialist maths

pikachu975 · Mar 20, 2017

maths methods said:
Is 3U maths like vce specialist maths

3U Maths is the second highest level of maths.

In NSW we have - General Maths (lowest), Mathematics (advanced), 3u maths, 4u maths.

Polynomials Question (1 Viewer)

boredofstudiesuser1

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integral95

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boredofstudiesuser1

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maths methods

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pikachu975

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