i dont understand this question:

in the quadratic equation x²+mx+2=0, the roots are consecutive. find the values of m.

i dont understand the part of the consecutive roots

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- Sep 2nd 2009, 12:58 AMpogiphilipsums and products of roots
i dont understand this question:

in the quadratic equation x²+mx+2=0, the roots are consecutive. find the values of m.

i dont understand the part of the consecutive roots - Sep 2nd 2009, 01:25 AMred_dog
The roots are $\displaystyle a$ and $\displaystyle a+1, \ a\in\mathbb{Z}$

Then $\displaystyle \left\{\begin{array}{ll}a+a+1=-m\\a(a+1)=2\end{array}\right.$

Solve the second equation, find a, then replace a in the first equation and find m. - Sep 2nd 2009, 01:31 AMpogiphilip
thanks for your help but i havent leant that so could you explain to me how that works?

- Sep 2nd 2009, 01:40 AMynj
- Sep 2nd 2009, 01:47 AMpogiphilip
i still dont understand what that is ynj

- Sep 2nd 2009, 02:03 AMynj
Do you know Vieta's Theorem?

if a quadratic equation $\displaystyle ax^2+bx+c=0$ have two roots $\displaystyle \alpha,\beta$, then $\displaystyle a(x-\alpha)(x-\beta)=ax^2+bx+c\Leftrightarrow ax^2-a(\alpha+\beta)x+a\alpha\beta=0$

Thus $\displaystyle \alpha+\beta=-\frac{b}{a},\alpha\beta=\frac{c}{a}$to keep all the coefficient identical.

So $\displaystyle a+(a+1)=-m,a(a+1)=2$,$\displaystyle (-m)^2-4\cdot 2=(a+(a+1))^2-4a(a+1)=(a-(a+1))^2=1$, Then you can solve m! - Sep 2nd 2009, 02:08 AMpogiphilip
but also the question says to use roots that are consecutive?, and i don't know vieta's theorem.

- Sep 2nd 2009, 02:10 AMynj
- Sep 2nd 2009, 02:40 AMpogiphilip
thank you for your help and i think i figured it out. thanks ynj and red_dog

- Sep 2nd 2009, 02:47 AMpogiphilip
also what are the roots if the two roots are consecutive?

- Sep 2nd 2009, 09:32 AMynj