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# Compute the sum of all the roots of (2x + 3)(x - 4) + (2x + 3)(x - 6)

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Math Expert
Joined: 02 Sep 2009
Posts: 54371
Compute the sum of all the roots of (2x + 3)(x - 4) + (2x + 3)(x - 6)  [#permalink]

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18 Mar 2019, 03:10
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:32) correct 29% (01:30) wrong based on 14 sessions

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Compute the sum of all the roots of (2x + 3)(x - 4) + (2x + 3)(x - 6) = 0

(A) 7/2
(B) 4
(C) 5
(D) 7
(E) 13

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Re: Compute the sum of all the roots of (2x + 3)(x - 4) + (2x + 3)(x - 6)  [#permalink]

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18 Mar 2019, 03:17
Bunuel wrote:
Compute the sum of all the roots of (2x + 3)(x - 4) + (2x + 3)(x - 6) = 0

(A) 7/2
(B) 4
(C) 5
(D) 7
(E) 13

2x+3 * ( x-4+x-6)=0
2x+3 * (2x-10)=0
so
x=-3/2 and 5
so sum
-3/2+5 ; 7/2
IMO A
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Compute the sum of all the roots of (2x + 3)(x - 4) + (2x + 3)(x - 6)  [#permalink]

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18 Mar 2019, 03:18
$$(2x+3)[x - 4 + x - 6] = 0$$
$$(2x + 3)[2x - 10] = 0$$
Solutions: $$x = {-\frac{3}{2}, 5}$$
Sum: $$\frac{10 - 3}{2} = \frac{7}{2}$$
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Compute the sum of all the roots of (2x + 3)(x - 4) + (2x + 3)(x - 6)   [#permalink] 18 Mar 2019, 03:18
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