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Quadratic eq

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by knight247 » Mon Sep 19, 2011 2:19 am
When a quadratic equation has only one root, in such a case the discriminant b²-4ac=0
In our equation a=3 b=n c=5. Substitute these values in the discriminant formula and you'll get
b=√60

Just remember, for any quadratic equation

b²-4ac>0 then the equation HAS TO HAVE TWO UNIQUE roots which are rational or irrational
b²-4ac=0 then the equation HAS ONLY ONE root which IS ALWAYS rational
b²-4ac<0 equation has no roots. Cheers.
Last edited by knight247 on Mon Sep 19, 2011 3:22 am, edited 1 time in total.
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by tdkk123 » Mon Sep 19, 2011 2:27 am
thanks a ton :)
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by gmatclubmember » Mon Sep 19, 2011 3:00 am
tdkk123 wrote:When 3x^2 + nx +5 = 0 has only one solution , n = ?

sqrt 60
It can have only one solution only if the equation is of the form (ax+b)^2=0.
So we can reduce the above equation to x^2+nx/3+5/3=0 => (x+Sqrt(5/3))^2=0 and so (coefficient of x) n/3=2sqrt(5/3) =>n=2sqrt(15)=>n=sqrt(60).

Cheers
Ami/-
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