Find Quadratic Equation From RootsDate: 9/15/96 at 16:36:41 From: Anonymous Subject: Find Quadratic Equation From Roots Write a quadratic equation with roots: -4 +/- sqrt(10) I figured out the sums by adding the two roots. I got -8 , which is right, but I can't figure out how to get the product. The answer should be 6. Date: 9/16/96 at 1:7:6 From: Doctor Pete Subject: Re: Find Quadratic Equation From Roots Okay, you know what the two roots are: p = -4 + Sqrt[10] q = -4 - Sqrt[10] and we want to find pq = (-4+Sqrt[10])(-4-Sqrt[10]). Now, here's a hint: (x+y)(x-y) = x^2 - y^2 (that is, x squared minus y squared). What if we let x = -4, y = Sqrt[10]? Now can you find the product pq? Of course, you probably already know that given the two roots, the quadratic equation is x^2 - (p+q)x + pq = 0. Still stumped? Feel free to ask for details. -Doctor Pete, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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