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

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Bunuel
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What is the product of the roots of x^2 – 7|x| - 30 = 0? [#permalink] New post   29 May 2020, 09:55
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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] New post   29 May 2020, 10:01
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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

ANswer: Option A
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Re: What is the product of the roots of x^2 – 7|x| - 30 = 0? [#permalink] New post   29 May 2020, 10:05
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\(x^2-7|x|-30\) ----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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Re: What is the product of the roots of x^2 – 7|x| - 30 = 0? [#permalink] New post   30 May 2020, 11:33
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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] New post   02 Aug 2020, 22:32
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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


Hi Bunuel,
Why cannot this equation be solved by definition? Product of roots = c/a for any quadratic equation ax^2+bx+c=0 ?
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AnkithaSrinivas
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Re: What is the product of the roots of x^2 – 7|x| - 30 = 0? [#permalink] New post   09 Jun 2021, 07:36
Doer01 wrote:
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


Hi Bunuel,
Why cannot this equation be solved by definition? Product of roots = c/a for any quadratic equation ax^2+bx+c=0 ?



cause there is modulus involved
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Re: What is the product of the roots of x^2 7|x| - 30 = 0? [#permalink] New post   06 Apr 2024, 14:27
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Re: What is the product of the roots of x^2 7|x| - 30 = 0? [#permalink]
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