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Re: What is the product of the roots of the equation y = |x|^2 - 5|x| + 6 [#permalink]
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When the equation is in the form of \(y=ax^2+bx+c\), the product of the roots of the equation is \(\frac{c}{a}\).

The equation in the question can be split into two different equations \(x^2-5x+6\) and \(x^2+5x+6\) when \(x>6\) and \(x<6\) respectively.

The final answer is the product of the products of roots of these two equations. In each equation, the product is \(6/1=6\). Hence the final answer is 36.
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Re: What is the product of the roots of the equation y = |x|^2 - 5|x| + 6 [#permalink]
Bunuel wrote:
What is the product of the roots of the equation \(y = |x|^2 - 5|x| + 6\)?

(A) -36
(B) 6
(C) -6
(D) 36
(E) 0


Are You Up For the Challenge: 700 Level Questions

Find the product of the roots of the equation \(y = |x|^2 - 5|x| + 6\), where |x| is the modulus of x.

Treat \(y = |x|^2 - 5|x| + 6\) as \(y = x^2 - 5x + 6\)

Or, \(y = x^2 -3x - 2x + 6\)

Or, \(y = x(x -3) - 2( x - 3)\)

Or, \(y = (x -3)(x - 2)\)

Now if \(y = 0\) we have \(x = 3 , 2\)

Now, initially we have assumed only the +ve values of \(y\), as \(3 , 2\), so the other possible values are \(-3 , -2\)

Thus, the product will be \(3*2*-3*-2 = 36\), Hence Answer must be (D)
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Re: What is the product of the roots of the equation y = |x|^2 - 5|x| + 6 [#permalink]
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Re: What is the product of the roots of the equation y = |x|^2 - 5|x| + 6 [#permalink]
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