Find the sum and product of the roots. 2x^2 + 6x - 8 = 0

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02-06-2017
Mathematics

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Find the sum and product of the roots. 2x^2 + 6x - 8 = 0

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LammettHash LammettHash · Answer 1 · 2017-06-02T21:54:59+02:00

LammettHash LammettHash

02-06-2017

Suppose you can factorize:

[tex]ax^2+bx+c=a(x-r_1)(x-r_2)[/tex]

Then by expanding the right side, you have

[tex]ax^2+bx+c=a(x^2-(r_1+r_2)x+r_1r_2)=ax^2-a(r_1+r_2)x+ar_1r_2[/tex]

which means in this case, you have to have

[tex]\begin{cases}6=-2(r_1+r_2)\\-8=2r_1r_2\end{cases}\implies\begin{cases}r_1+r_2=-3\\r_1r_2=-4\end{cases}[/tex]

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