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# If m and n are the roots of the quadratic equation x2 - (2 root 5)x -

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Joined: 02 Sep 2009
Posts: 49303
If m and n are the roots of the quadratic equation x2 - (2 root 5)x -  [#permalink]

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13 Mar 2016, 09:58
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Difficulty:

45% (medium)

Question Stats:

70% (01:26) correct 30% (02:11) wrong based on 83 sessions

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If m and n are the roots of the quadratic equation $$x^2 - (2 \sqrt 5)x - 2 = 0$$, the value of $$m^2 + n^2$$ is:

A. 18
B. 20
C. 22
D. 24
E. 32

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Joined: 25 Dec 2012
Posts: 121
Re: If m and n are the roots of the quadratic equation x2 - (2 root 5)x -  [#permalink]

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13 Mar 2016, 10:10
1
Bunuel wrote:
If m and n are the roots of the quadratic equation $$x^2 - (2 \sqrt 5)x - 2 = 0$$, the value of $$m^2 + n^2$$ is:

A. 18
B. 20
C. 22
D. 24
E. 32

Product of root, MN = C/A = -2/1 = -2
Sum of root, M+N = -B/A = -(-2\sqrt{5}/1 )= 2\sqrt{5}

(M+N)^2 = M^2 + N^2 + 2MN = 4*5 = 20

2MN = -2(2) = -4

M^2 + N^2 = 20 + 4 = 24

IMO .D
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Schools: Boston U '20 (M)
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Re: If m and n are the roots of the quadratic equation x2 - (2 root 5)x -  [#permalink]

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15 Mar 2016, 01:29
Senior Manager
Joined: 20 Aug 2015
Posts: 392
Location: India
GMAT 1: 760 Q50 V44
Re: If m and n are the roots of the quadratic equation x2 - (2 root 5)x -  [#permalink]

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15 Mar 2016, 05:17
1
3
Bunuel wrote:
If m and n are the roots of the quadratic equation $$x^2 - (2 \sqrt 5)x - 2 = 0$$, the value of $$m^2 + n^2$$ is:

A. 18
B. 20
C. 22
D. 24
E. 32

In the equation ax^2 + bx + c =0
Sum of roots = -b/a
Product of roots = c/a

Sum of roots (m + n) = $$(2 \sqrt 5)$$
Product of roots (mn) = -2

$$m^2 + n^2$$ = $$(m + n)^2 - 2mn$$ = 20 + 4 = 24
Option D
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Re: If m and n are the roots of the quadratic equation x2 - (2 root 5)x -  [#permalink]

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15 Jun 2016, 03:39
stonecold wrote:
Here D = B^2-AC = 28
so the roots are 2√5 +√28/2 and 2√5 -28/2
hence M^2 +N^2 => 28
i.e. D

Apology for seeing a typo error It should be 24 and not 28.
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Re: If m and n are the roots of the quadratic equation x2 - (2 root 5)x -  [#permalink]

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15 Jun 2016, 04:12
Bunuel wrote:
If m and n are the roots of the quadratic equation $$x^2 - (2 \sqrt 5)x - 2 = 0$$, the value of $$m^2 + n^2$$ is:

A. 18
B. 20
C. 22
D. 24
E. 32

m+n = -{- (2 \sqrt 5)}
mn = -2

Squaring 1st equation we get

$$m^2+n^2+2mn = 20$$

$$m^2+n^2= 20 - 2 *(-2)$$

$$m^2+n^2= 20 + 4$$ = 24

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Re: If m and n are the roots of the quadratic equation x2 - (2 root 5)x -  [#permalink]

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20 Aug 2018, 03:01
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Re: If m and n are the roots of the quadratic equation x2 - (2 root 5)x - &nbs [#permalink] 20 Aug 2018, 03:01
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