SOLUTION: find the quadratic equation whose roots is; three times the roots of 3x^2-10x+3=0

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Question 885979: find the quadratic equation whose roots is;
three times the roots of 3x^2-10x+3=0
Answer by basketball1127(19) About Me  (Show Source):
You can put this solution on YOUR website!
Let m and n be the roots of 3x^2-10x+3=0
Let p and q be the roots of the new quadratic equation(ax^2+bx+c)
Then 3m=p, 3n=q
m+n=-b%2F2a=-%28-10%29%2F2%283%29=10%2F6=5%2F3
mn= c%2Fa=3%2F3=1
so,
p+q = 3m+3n = 3(m+n) = 3(5/3) = 5
pq = (3m)(3n) = 9mn = 9(1) = 9
Since the new -b%2F2a = 5 and the new c%2Fa = 9
Then a=1 , b=-10 , c=9
so ax%5E2%2Bbx%2Bc = 1%28x%5E2%29%2B%28-10%29x%2B9 = x%5E2-10x%2B9