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Algebra Level 4

$\large |y|^2 - |y| - 12 = 0$

Give your answer as product of the real roots of $y$ .

The answer is -16.

1 solution

Caleb Townsend
Apr 4, 2015

$x = |y| \\ x^2 - x - 12 = 0 \\ (x-4)(x+3) = 0$ Clearly $x$ is either $4$ or $-3,$ but since $x = |y|,$ $x \geq 0$ so $x = 4.$ Now solve for $y.$ $|y| = 4 \\ y = \pm 4$ And finally, find the product of the solutions. $4\times (-4) = \boxed{-16}$

Right!!! That's how you do it!!

Vaibhav Kandwal - 6 years, 2 months ago

I entered 4 as the answer, since you asked for real roots

Ian Wong - 6 years, 2 months ago

$-4$ is a real root

Caleb Townsend - 6 years, 2 months ago

Mod's here! Mod's here!

The answer is -16.

1 solution

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