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# What is the product of the roots of x^2 – 7|x| - 30 = 0?

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Math Expert
Joined: 02 Sep 2009
Posts: 65062
What is the product of the roots of x^2 – 7|x| - 30 = 0?  [#permalink]

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29 May 2020, 08:55
00:00

Difficulty:

45% (medium)

Question Stats:

72% (01:56) correct 28% (01:43) wrong based on 79 sessions

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What is the product of the roots of $$x^2 – 7|x| - 30 = 0$$?

A. -100
B. -9
C. 0
D. 9
E. 100

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What is the product of the roots of x^2 – 7|x| - 30 = 0?  [#permalink]

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29 May 2020, 09:01
1
Bunuel wrote:
What is the product of the roots of $$x^2 – 7|x| - 30 = 0$$?

A. -100
B. -9
C. 0
D. 9
E. 100

$$x^2 – 7|x| - 30 = 0$$

i.e. $$lxl^2 – 7|x| - 30 = 0$$

i.e. $$lxl^2 – 10|x| + 3|x| - 30 = 0$$

i.e. $$(lxl – 10)*(|x| + 3) = 0$$

i.e lxl = 10 or -3

But lxl can NOT be negative hence it can NOT be -3

i.e. lxl = 10

i.e. x = +10 or -10

Product of the roots = (+10)*(-10) = -100

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Re: What is the product of the roots of x^2 – 7|x| - 30 = 0?  [#permalink]

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29 May 2020, 09:05
$$x^2-7|x|-30$$ ----eqn(1). We need to check for two values of |x|.

When x>0, solving eqn(1) we get x=10
When x<0, the value of x will be negation of what we obtained for x>0. Thus, we get x=-10.

Product of roots: -100.
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Joined: 11 Feb 2019
Posts: 308
Re: What is the product of the roots of x^2 – 7|x| - 30 = 0?  [#permalink]

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30 May 2020, 10:33
1
x^2–7|x|−30=0

Case 1: x> 0

x^2 -7x -30=0. => x^2 -10x +3x -30 =0
=> x = 10, -3; Since x >0, -3 is not possible

Case 2: x <0
x^2 +7x -30=0. => x^2 +10x -3x -30 =0
=> x = -10, 3; Since x<0 , 3 is not possible

Two roots: 10, -10

Product: -100

A
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Re: What is the product of the roots of x^2 – 7|x| - 30 = 0?   [#permalink] 30 May 2020, 10:33

# What is the product of the roots of x^2 – 7|x| - 30 = 0?

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