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# If equation x^2+bx+c=0 have two same roots, b=? (1) c=9 (2)

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If equation x^2+bx+c=0 have two same roots, b=? (1) c=9 (2) [#permalink]  21 Jun 2008, 18:16
20. If equation x^2+bx+c=0 have two same roots, b=?
(1) c=9
(2) the root is positive.

Peer
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peergmatclub wrote:
20. If equation x^2+bx+c=0 have two same roots, b=?
(1) c=9
(2) the root is positive.

Peer

Statement 1 x^2+bx+9=0 b can be -6 or 6; therefore, insufficient
Statement 2 the root is positive, b could equal lots of numbers
Together, x^2-6x+9=0 (x-3)^2=0 x=3 b=-6 sufficient
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C

Any quadratic equation ax^2+bx+c has two distinct roots when b^2-4ac > 0 , in case where the equation has the same root, b^2-4ac =0 ( which also implies that equation is a perfect square)

for our question a=1

Now

condition 1 c=9

b^2= 4*1*9 b = +/-6 , insuff

combining both, ifroot it +ve , b=-6 .
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