If 2b^2 + ac =0 then find the ratio of the zeroes of ax^2 + bx +c?
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let the zeroes be x, y
we know that sum of the roots x+y = -b/a and product of roots xy = c/a
(x+y)^2 = b^2/a^2
xy = c/a
given 2b^2 +ac =0
So 2x^2 + 2y^2 +4xy + xy = 0
2x^2 + 2y^2 +5xy = 0
2x(x+2y)+y(2y+x) = 0
(2x+y)(x+2y) = 0
so x/y ratio of zeroes is either -1/2 or -2
we know that sum of the roots x+y = -b/a and product of roots xy = c/a
(x+y)^2 = b^2/a^2
xy = c/a
given 2b^2 +ac =0
So 2x^2 + 2y^2 +4xy + xy = 0
2x^2 + 2y^2 +5xy = 0
2x(x+2y)+y(2y+x) = 0
(2x+y)(x+2y) = 0
so x/y ratio of zeroes is either -1/2 or -2
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