Question :
Give that α & β are roots of the equation 2x^{2 }+ 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
Question :
Give that α & β are roots of the equation 2x^{2 }+ 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
Vieta's formulas give us for the quadratic $\displaystyle ax^2+bx+c$ having roots $\displaystyle \alpha,\,\beta$:
$\displaystyle \alpha+\beta=-\frac{b}{a}$
$\displaystyle \alpha\beta=\frac{c}{a}$
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.
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
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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?