# Need help with roots of a equation

• Nov 18th 2012, 11:32 AM
L44
Need help with roots of a equation
Question :

Give that α & β are roots of the equation 2x2 + 5x - 7 = 0

Find without solving the equation the value of (α -β)2

Need to calculate the sum of the root and the product of the roots
• Nov 18th 2012, 11:48 AM
MarkFL
Re: Need help with roots of a equation
Vieta's formulas give us for the quadratic $\displaystyle ax^2+bx+c$ having roots $\displaystyle \alpha,\,\beta$:

$\displaystyle \alpha+\beta=-\frac{b}{a}$

$\displaystyle \alpha\beta=\frac{c}{a}$
• Nov 18th 2012, 11:50 AM
HallsofIvy
Re: Need help with roots of a equation
MarkFL meant to write $\displaystyle ax^2+ bx+ c$
• Nov 18th 2012, 11:59 AM
L44
Re: Need help with roots of a equation
I know that part i need to find the quadratic equation with the roots (α -β)2
• Nov 18th 2012, 12:09 PM
MarkFL
Re: Need help with roots of a equation
No, you need to find the value of $\displaystyle (\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta$.
• Nov 18th 2012, 12:12 PM
L44
Re: Need help with roots of a equation
Yeah I have that part as well the part I am not sure about is the sum of the root
• Nov 18th 2012, 12:20 PM
MarkFL
Re: Need help with roots of a equation
Since you are new here, I am going to give you a few tips:

1.) Don't double post. You have posted this topic in 2 different forums. This can lead to duplication of effort on the part of our contributors. You should choose the forum most appropriate for your question, and post it once there.

2.) Let us know what you have already done, and exactly where you are stuck. This avoids us telling you what you already know, and expedites the process.

So, you need the sum of the roots...you say you know Vieta's formulas, but these formulas give you just what you need, i.e., the sum and product of the roots.
• Nov 18th 2012, 12:34 PM
L44
Re: Need help with roots of a equation
well the double posting was not intentional I thought I placed the original post in the wrong thread where no one would see it.

I found α + β = -b/a = -5/2 while αβ = c/a = -7/2

the product of the root --> ((α -β)^2 = (α -β)(α -β) = (α+β)^2 - 4αβ= when you substitute the values where appropriate the final answer is 20.25
the sum of the root is (α -β) + (α -β) = 2α - 2β and this is the part that I am stuck
• Nov 18th 2012, 12:59 PM
MarkFL
Re: Need help with roots of a equation
In the future if you find you have posted in the wrong forum, you may use the report post function at the lower left of each post to report the post to the moderators and ask them to move the topic to the appropriate forum.

You have found that the requested expression is 20.25, which is correct. I don't understand why you are doing the additional step.

What is the problem in its entirety, exactly as given?