SOLUTION: find the quadratic equation whose roots is; square root of the roots of 4x^2-25x+36=0

Question 885980: find the quadratic equation whose roots is;
square root of the roots of 4x^2-25x+36=0
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
first you have to find the roots and then you have to figure out what to do with them based on the problem and then you have to find the factors that those roots were derived from and then you have to multiply those factors together to find the quadratic equation.
the following will show what what i mean.

start with:
4x^2 - 25x + 36 = 0
factor this equation to get:
(x-4) * (4x-9) = 0
solve for the roots to get:
x = 4 and x = 9/4
take the square root of these roots to get:
x = 2 and x = 3/2
convert these roots to factors as follows:
start with:
x = 2
subtract 2 from both sides of this equation to get:
x - 2 = 0
that's your first factor.
start with:
x = 3/2
multiply both sides of this equation by 2 to get:
2x = 3
subtract 3 from both sides of this equation to get:
2x - 3 = 0
that's your second factor.
multiply these factors together to get:
(x-2) * (2x-3) = 2x^2 - 7x + 6
that's your equation. set it equal to 0 and you get:
2x^2 - 7x + 6 = 0

i did not show you how to factor the quadratic equation.
here's a link that shows you the various methods used.
http://www.purplemath.com/modules/solvquad.htm
here's another that talks about the box method which is also helpful if the equation can be factored.
http://www.purplemath.com/modules/factquad2.htm
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