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# Find the value of 'b' if sqrt7 is a root of the equation x^2

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Find the value of 'b' if sqrt7 is a root of the equation x^2 [#permalink]

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30 Jan 2004, 16:20
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Find the value of 'b' if sqrt7 is a root of the equation x^2 + ax - 14 = 0 and the equation x^2 + ax + b = 0 has real and equal roots.

7/4
-7/4
49/4

none of these
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30 Jan 2004, 16:29
from the second eqn: equal and real roots
a^2 = 4b

from the first eqn, let k be the other root

sqrt(7)+ k = - a
ksqrt(7) = -14

Thus b = (1/4)[sqrt(7) - [14/sqrt(7)]]^2

Last edited by Zhung Gazi on 30 Jan 2004, 17:12, edited 1 time in total.

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Senior Manager
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30 Jan 2004, 16:33

Rakesh, we did a similar problem yesterday, but I am having problems with this question. Can u help
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30 Jan 2004, 16:54
Yeah ur posting such wonderful avathars. We go step by step

from the first eq. let p & q be the roots then we know that p+q= - b/a (the eq is of the form ax^2 + bx +c ), so p+q = -a/1 = -a ( eq is x^2+ax-14) and pq = c/a = -14, we are given that one root is sqrt7 then let p=sqrt7 , we know that pq=-14, so (sqrt7* q) = -14 solve and we get q = -2sqrt7, we also know that p =sqrt7 and p+q = -a, substitute the values of p & q and we get a=sqrt7----------------(1)

from the second eq, we r given that it has real and equal roots so it means b^2- 4ac=0 ( for eq of the form ax^2 +bx +c) so as the given eq is of the form x^2 +ax+b=0 , we get a^2 - 4 * 1 * b=0, so a^2=4b, we know that a=sqrt7 ( from -----(1) above) substitute this value of a in a^2=4b and we get b=7/4.

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Senior Manager
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30 Jan 2004, 17:32

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Pls include reasoning along with all answer posts.
****GMAT Loco****
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30 Jan 2004, 17:32
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# Find the value of 'b' if sqrt7 is a root of the equation x^2

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