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Find the value of 'a' and 'b' if sq root of 3 is a root of

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sunniboy007
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Find the value of 'a' and 'b' if sq root of 3 is a root of [#permalink] New post   26 Jan 2004, 16:54
Find the value of 'a' and 'b' if sq root of 3 is a root of the equation
x^2 +ax - 6 = 0
and the equation x^2 +ax + b = 0 has real and equal roots.



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Re: Find the value of 'a' and 'b' if sq root of 3 is a root of [#permalink] New post   26 Jan 2004, 17:13
a= sqrt 3 and b= 3/4, when the euation has real and equal roots then D=0 ie b^2-4ac=0, we know that b=a, a=1 and c=b then by substituting we get a^2-4b=0, ie a^2=4b-----------(1)


we are given that sum of roots= -a and product = -6 let x and y be the roots then x+y=-a and xy= -6 and also we are given that x= sqrt3 so by substituting we get a= sqrt 3 and by substituting this value in eq (1) above we get b= 3/4
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Re: Find the value of 'a' and 'b' if sq root of 3 is a root of [#permalink] New post   26 Jan 2004, 17:26
Your answer is correct, but
why does c=b , and not c=-6?
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Re: Find the value of 'a' and 'b' if sq root of 3 is a root of [#permalink] New post   26 Jan 2004, 17:35
in the first equation we r already given one root so we find out the other root and in the second equation its given that the roots are real and equal so D which is the discriminant= 0 and we know that D=b^2-4ac for a quad eq of the form ax^2 + bx +c =0
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Re: Find the value of 'a' and 'b' if sq root of 3 is a root of [#permalink] New post   29 Jan 2004, 13:40
a = sqrt(3)
and b >= 3/4
( if b = 3/4 ) then the second eq has real and equal roots
( if b > 3/4 ) then the eq has no equal and real roots

for first eq this is what I did

x^2+ax-6 = (x+sqrt(3) ) ( x+k )

x^2+x(k-sqrt(3))-k*sqrt(3) = x^2+ax-6
so k*sqrt(3) = 6 hence k = 2*sqrt(3)
so a = sqrt(3)
substitute value of a in second equation and find the roots



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Re: Find the value of 'a' and 'b' if sq root of 3 is a root of [#permalink]
29 Jan 2004, 13:40
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